Sharp Spectral Gap Estimates on Manifolds under Integral Ricci Curvature Bounds

TL;DR

This paper establishes precise spectral gap estimates for compact manifolds with integral Ricci curvature bounds, extending previous results and confirming a recent conjecture for dimensions three and higher.

Contribution

It generalizes classical spectral gap estimates to manifolds with integral Ricci curvature bounds, advancing the understanding of geometric analysis under weaker curvature conditions.

Findings

Proves sharp spectral gap estimates under integral curvature bounds

Extends Kröger's and Bakry-Qian's results to new curvature conditions

Confirms a recent conjecture for dimensions n ≥ 3

Abstract

We prove sharp spectral gap estimates on compact manifolds with integral curvature bounds. We generalize the results of Kr\"oger (Kr\"oger '92) as well as of Bakry and Qian (Bakry-Qian '00) to the case of integral curvature and confirm the conjecture in (Ramos et al. '20) for the case $n \geq 3$.