---
res:
  bibo_abstract:
  - 'We extend the notion of the minimal volume ellipsoid containing a convex body
    in Rd to the setting of logarithmically concave functions. We consider a vast
    class of logarithmically concave functions whose superlevel sets are concentric
    ellipsoids. For a fixed function from this class, we consider the set of all its
    “affine” positions. For any log-concave function f on Rd, we consider functions
    belonging to this set of “affine” positions, and find the one with the minimal
    integral under the condition that it is pointwise greater than or equal to f.
    We study the properties of existence and uniqueness of the solution to this problem.
    For any s∈[0,+∞), we consider the construction dual to the recently defined John
    s-function (Ivanov and Naszódi in Functional John ellipsoids. arXiv preprint:
    arXiv:2006.09934, 2020). We prove that such a construction determines a unique
    function and call it the Löwner s-function of f. We study the Löwner s-functions
    as s tends to zero and to infinity. Finally, extending the notion of the outer
    volume ratio, we define the outer integral ratio of a log-concave function and
    give an asymptotically tight bound on it.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Grigory
      foaf_name: Ivanov, Grigory
      foaf_surname: Ivanov
      foaf_workInfoHomepage: http://www.librecat.org/personId=87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  - foaf_Person:
      foaf_givenName: Igor
      foaf_name: Tsiutsiurupa, Igor
      foaf_surname: Tsiutsiurupa
  bibo_doi: 10.1007/s12220-021-00691-4
  bibo_volume: 31
  dct_date: 2021^xs_gYear
  dct_identifier:
  - UT:000656507500001
  dct_isPartOf:
  - http://id.crossref.org/issn/1050-6926
  - http://id.crossref.org/issn/1559-002X
  dct_language: eng
  dct_publisher: Springer@
  dct_title: Functional Löwner ellipsoids@
...