Upper bounds on the size of nodal sets for Gevrey and quasianalytic Riemannian manifolds

2022/05/01 by Hamid Hezari, Hezari, Hamid
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2205.00398

openalex publication_date 2022/05/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We find new polynomial upper bounds for the size of nodal sets of eigenfunctions when the Riemannian manifold has a Gevrey or quasianalytic regularity.

Related

• The size of the nodal sets for the eigenfunctions of the smooth laplacian
• Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
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• Some remarks on nodal geometry in the smooth setting
• Distribution of the nodal sets of eigenfunctions on analytic manifolds