Sharp Spectral Gaps on Metric Measure Spaces
Yin Jiang, Hui-Chun Zhang

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).
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations
