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arXiv:2406.16036 [math.AP]AbstractReferencesReviewsResources

Sharp local Bernstein estimates for Laplace eigenfunctions on Riemannian manifolds

Kévin Le Balc'h

Published 2024-06-23Version 1

In this paper we focus on local growth properties of Laplace eigenfunctions on a compact Riemannian manifold. The principal theme is that a Laplace eigenfunction behaves locally as a polynomial function of degree proportional to the square root of the eigenvalue. In this direction, we notably prove sharp local Bernstein estimates, conjectured by Donnelly and Fefferman in 1990.

Comments: Comments are welcome
Categories: math.AP, math.CA, math.DG, math.SP
Subjects: 58J50, 35J05, 35P20, 35R01
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