# Estimates for Sums and Gaps of Eigenvalues of Laplacians on Measure Spaces

New publication by Sze-Man Ngai:

Abstract: For Laplacians defined by measures on a bounded domain in Rn, we prove analogs of the classical eigenvalue estimates for the standard Laplacian: lower bound of sums of eigenvalues by Li and Yau, and gaps of consecutive eigenvalues by Payne, Polya and Weinberger. This work is motivated by the study of spectral gaps for Laplacians on fractals.