--- _id: '74' abstract: - lang: eng text: "We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about \ the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily \ radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument \ to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures." article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: 'Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1' apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1 chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1. ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27. ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27.' mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1. short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27. date_created: 2018-12-11T11:44:29Z date_published: 2020-06-21T00:00:00Z date_updated: 2023-08-17T13:48:31Z day: '21' department: - _id: HeEd - _id: JaMa doi: 10.1007/978-3-030-36020-7_1 ec_funded: 1 editor: - first_name: Bo'az full_name: Klartag, Bo'az last_name: Klartag - first_name: Emanuel full_name: Milman, Emanuel last_name: Milman external_id: arxiv: - '1808.07350' isi: - '000557689300003' intvolume: ' 2256' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.07350 month: '06' oa: 1 oa_version: Preprint page: 1-27 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Geometric Aspects of Functional Analysis publication_identifier: eisbn: - '9783030360207' eissn: - '16179692' isbn: - '9783030360191' issn: - '00758434' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNM status: public title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures type: book_chapter user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 2256 year: '2020' ...