Sharp Spectral Gaps on Metric Measure Spaces

TL;DR

This paper extends sharp spectral gap bounds from smooth manifolds to general metric measure spaces satisfying the RCD*(K,N) condition, broadening the applicability of these bounds in geometric analysis.

Contribution

It generalizes existing spectral gap bounds to metric measure spaces with Riemannian curvature-dimension conditions, unifying and extending previous results.

Findings

Established sharp spectral gap bounds for RCD*(K,N) spaces.

Unified framework for spectral gap estimates across different geometric settings.

Extended classical bounds to non-smooth metric measure spaces.

Abstract

In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to general metric measure spaces with Riemannian curvature-dimension condition RCD*(K;N).