Sharp local Bernstein estimates for Laplace eigenfunctions on Riemannian manifolds
arxiv(2024)
摘要
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.
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