Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Kei Funano; Yohei Sakurai

doi:10.1090/proc/14430

Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Kei Funano, Yohei Sakurai

INF - System Information Sciences

Tohoku University

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

2 Citations (Scopus)

Abstract

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponen-tially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type L_p moment estimates of eigenfunctions.

Original language	English
Pages (from-to)	3155-3164
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	7
DOIs	https://doi.org/10.1090/proc/14430
Publication status	Published - 2019

Keywords

Concentration
Eigenfunctions
Nodal set
Ricci curvature

Access to Document

10.1090/proc/14430

Cite this

@article{d38e8d0c83c84f46a70c213c91fc58b8,

title = "Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold",

abstract = "We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponen-tially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type Lp moment estimates of eigenfunctions.",

keywords = "Concentration, Eigenfunctions, Nodal set, Ricci curvature",

author = "Kei Funano and Yohei Sakurai",

note = "Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

doi = "10.1090/proc/14430",

language = "English",

volume = "147",

pages = "3155--3164",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

AU - Funano, Kei

AU - Sakurai, Yohei

PY - 2019

Y1 - 2019

N2 - We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponen-tially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type Lp moment estimates of eigenfunctions.

AB - We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponen-tially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type Lp moment estimates of eigenfunctions.

KW - Concentration

KW - Eigenfunctions

KW - Nodal set

KW - Ricci curvature

UR - http://www.scopus.com/inward/record.url?scp=85070622432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070622432&partnerID=8YFLogxK

U2 - 10.1090/proc/14430

DO - 10.1090/proc/14430

M3 - Article

AN - SCOPUS:85070622432

SN - 0002-9939

VL - 147

SP - 3155

EP - 3164

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this