Curvature and harmonic analysis on compact manifolds

Fuente: arXiv
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Autor principal: Sogge, Christopher D.
Formato: Preprint
Publicado: 2024
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author Sogge, Christopher D.
author_facet Sogge, Christopher D.
contents We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $L^q$-estimates, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, of log-quasimodes that characterize compact connected space forms in terms of the growth rate of $L^q$-norms of such quasimode for these relatively small Lebesgue exponents $q$. No such characterization is possible for any exponent $q> q_c$.
format Preprint
id arxiv_https___arxiv_org_abs_2404_13739
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Curvature and harmonic analysis on compact manifolds
Sogge, Christopher D.
Analysis of PDEs
Classical Analysis and ODEs
Differential Geometry
58J50, 35P15
We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $L^q$-estimates, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, of log-quasimodes that characterize compact connected space forms in terms of the growth rate of $L^q$-norms of such quasimode for these relatively small Lebesgue exponents $q$. No such characterization is possible for any exponent $q> q_c$.
title Curvature and harmonic analysis on compact manifolds
topic Analysis of PDEs
Classical Analysis and ODEs
Differential Geometry
58J50, 35P15
url https://arxiv.org/abs/2404.13739