Isoperimetric clusters in homogeneous spaces via concentration compactness

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Isoperimetric clusters in homogeneous spaces via concentration compactness. / Novaga, Matteo; Paolini, Emanuele; Stepanov, Eugene; Tortorelli, Vincenzo.

In: Journal of Geometric Analysis, Vol. 32, No. 11, 263, 11.2022.

Research output: Contribution to journal › Article › peer-review

Author

Novaga, Matteo ; Paolini, Emanuele ; Stepanov, Eugene ; Tortorelli, Vincenzo. / Isoperimetric clusters in homogeneous spaces via concentration compactness. In: Journal of Geometric Analysis. 2022 ; Vol. 32, No. 11.

BibTeX

@article{cd53ea1211434942a2e5123a1d9d6c90,

title = "Isoperimetric clusters in homogeneous spaces via concentration compactness",

abstract = "We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms, for a quite wide range of perimeter functionals. Such generalized clusters are a natural “relaxed” version of a cluster and can be thought of as “albums” with possibly infinite pages, having a minimal cluster drawn on each page, the total perimeter and the vector of masses being calculated by summation over all pages, the total perimeter being minimal among all generalized clusters with the same masses. The examples include any anisotropic perimeter in a Euclidean space, as well as a hyperbolic plane with the Riemannian perimeter and Heisenberg groups with a canonical left invariant perimeter or its equivalent versions.",

keywords = "Primary 53C65, Secondary 49Q15, 60H05, Isoperimetric sets, Homogeneous space, Isoperimetric clusters",

author = "Matteo Novaga and Emanuele Paolini and Eugene Stepanov and Vincenzo Tortorelli",

note = "Novaga, M., Paolini, E., Stepanov, E. et al. Isoperimetric Clusters in Homogeneous Spaces via Concentration Compactness. J Geom Anal 32, 263 (2022). https://doi.org/10.1007/s12220-022-01009-8 Publisher Copyright: {\textcopyright} 2022, Mathematica Josephina, Inc.",

year = "2022",

month = nov,

doi = "10.1007/s12220-022-01009-8",

language = "English",

volume = "32",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer Nature",

number = "11",

}

RIS

TY - JOUR

T1 - Isoperimetric clusters in homogeneous spaces via concentration compactness

AU - Novaga, Matteo

AU - Paolini, Emanuele

AU - Stepanov, Eugene

AU - Tortorelli, Vincenzo

N1 - Novaga, M., Paolini, E., Stepanov, E. et al. Isoperimetric Clusters in Homogeneous Spaces via Concentration Compactness. J Geom Anal 32, 263 (2022). https://doi.org/10.1007/s12220-022-01009-8 Publisher Copyright: © 2022, Mathematica Josephina, Inc.

PY - 2022/11

Y1 - 2022/11

N2 - We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms, for a quite wide range of perimeter functionals. Such generalized clusters are a natural “relaxed” version of a cluster and can be thought of as “albums” with possibly infinite pages, having a minimal cluster drawn on each page, the total perimeter and the vector of masses being calculated by summation over all pages, the total perimeter being minimal among all generalized clusters with the same masses. The examples include any anisotropic perimeter in a Euclidean space, as well as a hyperbolic plane with the Riemannian perimeter and Heisenberg groups with a canonical left invariant perimeter or its equivalent versions.

AB - We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms, for a quite wide range of perimeter functionals. Such generalized clusters are a natural “relaxed” version of a cluster and can be thought of as “albums” with possibly infinite pages, having a minimal cluster drawn on each page, the total perimeter and the vector of masses being calculated by summation over all pages, the total perimeter being minimal among all generalized clusters with the same masses. The examples include any anisotropic perimeter in a Euclidean space, as well as a hyperbolic plane with the Riemannian perimeter and Heisenberg groups with a canonical left invariant perimeter or its equivalent versions.

KW - Primary 53C65

KW - Secondary 49Q15

KW - 60H05

KW - Isoperimetric sets

KW - Homogeneous space

KW - Isoperimetric clusters

UR - https://link.springer.com/article/10.1007/s12220-022-01009-8

UR - http://www.scopus.com/inward/record.url?scp=85136501872&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3de5641c-6221-3438-8696-81e6c7f6fa23/

U2 - 10.1007/s12220-022-01009-8

DO - 10.1007/s12220-022-01009-8

M3 - Article

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 11

M1 - 263

ER -

ID: 100611857