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Curvature and harmonic analysis on compact manifolds

Published 21 Apr 2024 in math.AP, math.CA, and math.DG | (2404.13739v1)

Abstract: We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $Lq$-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 $Lq$-norms of such quasimode for these relatively small Lebesgue exponents $q$. No such characterization is possible for any exponent $q> q_c$.

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