Critical set of eigenfunctions of the Laplacian

Abstract

We give an upper bound for the $(n-1)$-dimensional Hausdorff measure of the critical set of eigenfunctions of the Laplacian on compact analytic Riemannian manifolds. This is the analog of H. Donnely and C. Fefferman result on nodal set of eigenfunctions.

21 pages

References in corpus (2)

• Lower bounds for nodal sets of eigenfunctions
• Quantitative uniqueness for Schrödinger operator

Cited by in corpus (1)

• Eigenfunctions and Nodal Sets