Weyl law for the volume spectrum

Yevgeny Liokumovich; Fernando C. Marques; André Neves

doi:10.4007/annals.2018.187.3.7

Weyl law for the volume spectrum

Yevgeny Liokumovich
, Fernando C. Marques
, André Neves

Mathematics

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

79 Scopus citations

Abstract

Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum [ωp(M)]_ρ∈ℕ satisfies a Weyl law that was conjectured by Gromov.

Original language	English (US)
Pages (from-to)	933-961
Number of pages	29
Journal	Annals of Mathematics
Volume	187
Issue number	3
DOIs	https://doi.org/10.4007/annals.2018.187.3.7
State	Published - May 1 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Lusternik-Schnirelmann
Min-max
Volume spectrum
Weyl law

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10.4007/annals.2018.187.3.7

Cite this

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title = "Weyl law for the volume spectrum",

abstract = "Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum [ωp(M)]ρ∈ℕ satisfies a Weyl law that was conjectured by Gromov.",

keywords = "Lusternik-Schnirelmann, Min-max, Volume spectrum, Weyl law",

author = "Yevgeny Liokumovich and Marques, \{Fernando C.\} and Andr{\'e} Neves",

note = "Publisher Copyright: {\textcopyright} 2018 Department of Mathematics, Princeton University.",

year = "2018",

month = may,

day = "1",

doi = "10.4007/annals.2018.187.3.7",

language = "English (US)",

volume = "187",

pages = "933--961",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Department of Mathematics at Princeton University",

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TY - JOUR

T1 - Weyl law for the volume spectrum

AU - Liokumovich, Yevgeny

AU - Marques, Fernando C.

AU - Neves, André

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum [ωp(M)]ρ∈ℕ satisfies a Weyl law that was conjectured by Gromov.

AB - Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum [ωp(M)]ρ∈ℕ satisfies a Weyl law that was conjectured by Gromov.

KW - Lusternik-Schnirelmann

KW - Min-max

KW - Volume spectrum

KW - Weyl law

UR - https://www.scopus.com/pages/publications/85048604317

UR - https://www.scopus.com/pages/publications/85048604317#tab=citedBy

U2 - 10.4007/annals.2018.187.3.7

DO - 10.4007/annals.2018.187.3.7

M3 - Article

AN - SCOPUS:85048604317

SN - 0003-486X

VL - 187

SP - 933

EP - 961

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -

Weyl law for the volume spectrum

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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