Neumann spectral cluster estimates outside convex obstacles

TL;DR

This paper establishes $L^p$ norm estimates for spectral clusters of the Neumann Laplacian on manifolds with concave boundaries, advancing understanding of spectral behavior in geometric analysis.

Contribution

It provides new inequalities controlling spectral cluster norms for Neumann Laplacians on manifolds with concave boundaries, extending previous spectral estimates.

Findings

Proved $L^p$ bounds for spectral clusters

Extended spectral estimates to manifolds with concave boundaries

Enhanced understanding of Neumann Laplacian spectral behavior

Abstract

This paper concerns spectral clusters of the Neumann Laplacian on compact Riemannian manifolds with strictly geodesically concave boundary. We prove an inequality which controls the $L^p$ norms of spectral clusters.