---
OA_place: publisher
OA_type: gold
_id: '22003'
abstract:
- lang: eng
  text: 'Let G be a finite, connected metric graph and let X be a subset of G. If
    X is sufficiently dense in G, we show that the Gromov-Hausdorff distance matches
    the Hausdorff distance, namely d_GH(G,X) = d_H(G,X). When the metric graph is
    the circle G = S¹ with circumference 2π, a recent study established the equality
    d_GH(S¹,X) = d_H(S¹,X) whenever d_GH(S¹,X) < π/6. Our results relax this hypothesis
    to d_GH(S¹,X) < π/3, and furthermore, we show that the constant π/3 is the best
    possible. We lower bound the Gromov-Hausdorff distance d_GH(G,X) by the Hausdorff
    distance d_H(G,X) via a simple topological obstruction: the existence of a possibly
    discontinuous function f: G → X with too small distortion contradicts the connectedness
    of G.'
acknowledgement: "Funding Henry Adams: Simons Foundation Travel Support for Mathematicians.\r\nŽiga
  Virk: Slovene research agency grant P1-0292.\r\nNicolò Zava: FWF Grant, Project
  number I4245-N35.\r\n"
alternative_title:
- LIPIcs
article_number: 3:1-3:16
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Henry
  full_name: Adams, Henry
  last_name: Adams
- first_name: Sushovan
  full_name: Majhi, Sushovan
  last_name: Majhi
- first_name: Fedor
  full_name: Manin, Fedor
  last_name: Manin
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Nicolò
  full_name: Zava, Nicolò
  id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
  last_name: Zava
  orcid: 0000-0001-8686-1888
citation:
  ama: 'Adams H, Majhi S, Manin F, Virk Z, Zava N. Lower bounding the Gromov–Hausdorff
    distance in metric graphs. In: <i>42nd International Symposium on Computational
    Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026.
    doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">10.4230/LIPIcs.SoCG.2026.3</a>'
  apa: 'Adams, H., Majhi, S., Manin, F., Virk, Z., &#38; Zava, N. (2026). Lower bounding
    the Gromov–Hausdorff distance in metric graphs. In <i>42nd International Symposium
    on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss
    Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a>'
  chicago: Adams, Henry, Sushovan Majhi, Fedor Manin, Ziga Virk, and Nicolò Zava.
    “Lower Bounding the Gromov–Hausdorff Distance in Metric Graphs.” In <i>42nd International
    Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik, 2026. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a>.
  ieee: H. Adams, S. Majhi, F. Manin, Z. Virk, and N. Zava, “Lower bounding the Gromov–Hausdorff
    distance in metric graphs,” in <i>42nd International Symposium on Computational
    Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.
  ista: 'Adams H, Majhi S, Manin F, Virk Z, Zava N. 2026. Lower bounding the Gromov–Hausdorff
    distance in metric graphs. 42nd International Symposium on Computational Geometry.
    SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 3:1-3:16.'
  mla: Adams, Henry, et al. “Lower Bounding the Gromov–Hausdorff Distance in Metric
    Graphs.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367,
    3:1-3:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.3">10.4230/LIPIcs.SoCG.2026.3</a>.
  short: H. Adams, S. Majhi, F. Manin, Z. Virk, N. Zava, in:, 42nd International Symposium
    on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2026.
conference:
  end_date: 2026-06-05
  location: New Brunswick, NJ, United States
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-06-14T22:01:44Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-06-22T08:49:17Z
day: '27'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2026.3
external_id:
  arxiv:
  - '2411.09182'
file:
- access_level: open_access
  checksum: 25d27c016409563196b8aecfe5bfdf41
  content_type: application/pdf
  creator: dernst
  date_created: 2026-06-22T08:43:47Z
  date_updated: 2026-06-22T08:43:47Z
  file_id: '22115'
  file_name: 2026_LIPIcSSoCG_Adams.pdf
  file_size: 1091310
  relation: main_file
  success: 1
file_date_updated: 2026-06-22T08:43:47Z
fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2026.3
has_accepted_license: '1'
intvolume: '       367'
keyword:
- Gromov–Hausdorff distance
- distortion
- connectedness
- Borsuk–Ulam theorem
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
  eissn:
  - 1868-8969
  isbn:
  - '9783959774185'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounding the Gromov–Hausdorff distance in metric graphs
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...
---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '20867'
abstract:
- lang: eng
  text: We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which
    consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff
    distance, into Hilbert spaces. These embeddings are particularly valuable for
    applications to topological data analysis. We prove that its subspace consisting
    of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus,
    there exists a coarse embedding of that space into a Hilbert space. On the contrary,
    if the number of points is not bounded, then the subspace cannot be coarsely embedded
    into any uniformly convex Banach space and so, in particular, into any Hilbert
    space. Furthermore, we prove that, even if we restrict to finite metric spaces
    whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz
    embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability
    results by finding obstructions to coarse and bi-Lipschitz embeddings in families
    of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff
    distance.
acknowledgement: "The author was supported by the FWF Grant, Project number I4245-N35.
  The author would like to thank Thomas Weighill for the helpful discussions around
  Theorem 3.10, and Takamitsu Yamauchi for bringing to my attention the fundamental
  reference [35]. Furthermore, the author\r\nis thankful for the detailed and helpful
  comments of the reviewer of this manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolò
  full_name: Zava, Nicolò
  id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
  last_name: Zava
  orcid: 0000-0001-8686-1888
citation:
  ama: Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
    space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>. 2025;25(8):5153-5174.
    doi:<a href="https://doi.org/10.2140/agt.2025.25.5153">10.2140/agt.2025.25.5153</a>
  apa: Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the
    Gromov–Hausdorff space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>.
    Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/agt.2025.25.5153">https://doi.org/10.2140/agt.2025.25.5153</a>
  chicago: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the
    Gromov–Hausdorff Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>.
    Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/agt.2025.25.5153">https://doi.org/10.2140/agt.2025.25.5153</a>.
  ieee: N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
    space into Hilbert spaces,” <i>Algebraic &#38; Geometric Topology</i>, vol. 25,
    no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025.
  ista: Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
    space into Hilbert spaces. Algebraic &#38; Geometric Topology. 25(8), 5153–5174.
  mla: Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff
    Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>, vol. 25,
    no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:<a href="https://doi.org/10.2140/agt.2025.25.5153">10.2140/agt.2025.25.5153</a>.
  short: N. Zava, Algebraic &#38; Geometric Topology 25 (2025) 5153–5174.
corr_author: '1'
date_created: 2025-12-29T12:09:09Z
date_published: 2025-11-20T00:00:00Z
date_updated: 2026-01-05T12:19:09Z
day: '20'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.2140/agt.2025.25.5153
external_id:
  arxiv:
  - '2303.04730'
file:
- access_level: open_access
  checksum: 1e05b4f17a44500ae1ae1e21bc636f6a
  content_type: application/pdf
  creator: dernst
  date_created: 2026-01-05T12:16:38Z
  date_updated: 2026-01-05T12:16:38Z
  file_id: '20943'
  file_name: 2025_AlgebraicGeomTopology_Zava.pdf
  file_size: 574389
  relation: main_file
  success: 1
file_date_updated: 2026-01-05T12:16:38Z
fulldoi: https://doi.org/10.2140/agt.2025.25.5153
has_accepted_license: '1'
intvolume: '        25'
issue: '8'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5153-5174
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Algebraic & Geometric Topology
publication_identifier:
  eissn:
  - 1472-2739
  issn:
  - 1472-2747
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff
  space into Hilbert spaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2025'
...
---
_id: '12764'
abstract:
- lang: eng
  text: We study a new discretization of the Gaussian curvature for polyhedral surfaces.
    This discrete Gaussian curvature is defined on each conical singularity of a polyhedral
    surface as the quotient of the angle defect and the area of the Voronoi cell corresponding
    to the singularity. We divide polyhedral surfaces into discrete conformal classes
    using a generalization of discrete conformal equivalence pioneered by Feng Luo.
    We subsequently show that, in every discrete conformal class, there exists a polyhedral
    surface with constant discrete Gaussian curvature. We also provide explicit examples
    to demonstrate that this surface is in general not unique.
acknowledgement: Open access funding provided by the Austrian Science Fund (FWF).
  This research was supported by the FWF grant, Project number I4245-N35, and by the
  Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID
  195170736 - TRR109.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
  orcid: 0000-0001-7841-0091
citation:
  ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. <i>Discrete and
    Computational Geometry</i>. 2023;70:123-153. doi:<a href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>
  apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. <i>Discrete
    and Computational Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>
  chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>.
  ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete
    and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023.
  ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
    and Computational Geometry. 70, 123–153.
  mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 123–53, doi:<a
    href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>.
  short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
corr_author: '1'
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2025-04-23T08:59:15Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
  isi:
  - '000948148000001'
  pmid:
  - '37292248'
file:
- access_level: open_access
  checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3
  content_type: application/pdf
  creator: dernst
  date_created: 2023-10-04T11:46:24Z
  date_updated: 2023-10-04T11:46:24Z
  file_id: '14396'
  file_name: 2023_DiscreteGeometry_Kourimska.pdf
  file_size: 1026683
  relation: main_file
  success: 1
file_date_updated: 2023-10-04T11:46:24Z
fulldoi: https://doi.org/10.1007/s00454-023-00484-2
has_accepted_license: '1'
intvolume: '        70'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 123-153
pmid: 1
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Discrete and Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete yamabe problem for polyhedral surfaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2023'
...
---
_id: '14557'
abstract:
- lang: eng
  text: Motivated by a problem posed in [10], we investigate the closure operators
    of the category SLatt of join semilattices and its subcategory SLattO of join
    semilattices with bottom element. In particular, we show that there are only finitely
    many closure operators of both categories, and provide a complete classification.
    We use this result to deduce the known fact that epimorphisms of SLatt and SLattO
    are surjective. We complement the paper with two different proofs of this result
    using either generators or Isbell’s zigzag theorem.
acknowledgement: "The first and second named authors are members of GNSAGA – INdAM.\r\nThe
  third named author was supported by the FWF Grant, Project number I4245–N35"
article_processing_charge: No
article_type: original
author:
- first_name: D.
  full_name: Dikranjan, D.
  last_name: Dikranjan
- first_name: A.
  full_name: Giordano Bruno, A.
  last_name: Giordano Bruno
- first_name: Nicolò
  full_name: Zava, Nicolò
  id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
  last_name: Zava
  orcid: 0000-0001-8686-1888
citation:
  ama: Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of
    categories of semilattices. <i>Quaestiones Mathematicae</i>. 2023;46(S1):191-221.
    doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a>
  apa: Dikranjan, D., Giordano Bruno, A., &#38; Zava, N. (2023). Epimorphisms and
    closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>.
    Taylor &#38; Francis. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a>
  chicago: Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure
    Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>. Taylor
    &#38; Francis, 2023. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a>.
  ieee: D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators
    of categories of semilattices,” <i>Quaestiones Mathematicae</i>, vol. 46, no.
    S1. Taylor &#38; Francis, pp. 191–221, 2023.
  ista: Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators
    of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.
  mla: Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of
    Semilattices.” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1, Taylor &#38;
    Francis, 2023, pp. 191–221, doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a>.
  short: D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023)
    191–221.
date_created: 2023-11-19T23:00:55Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:23:12Z
day: '01'
department:
- _id: HeEd
doi: 10.2989/16073606.2023.2247731
external_id:
  isi:
  - '001098712000006'
fulldoi: https://doi.org/10.2989/16073606.2023.2247731
intvolume: '        46'
isi: 1
issue: S1
language:
- iso: eng
month: '11'
oa_version: None
page: 191-221
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Quaestiones Mathematicae
publication_identifier:
  eissn:
  - 1727-933X
  issn:
  - 1607-3606
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Epimorphisms and closure operators of categories of semilattices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 46
year: '2023'
...