Eigenvalue estimates and L1 energy on closed manifolds
Li Ma
TL;DR
This paper investigates eigenvalue estimates and energy bounds for the drifting Laplacian on closed manifolds, extending classical results to weighted measures and Ricci solitons.
Contribution
It provides new eigenvalue estimates and energy inequalities for the drifting Laplacian on weighted closed manifolds, including Ricci solitons.
Findings
Lichnerowicz type eigenvalue estimates derived
L1 and L2 energy bounds established for drifting heat equations
Results applicable to Ricci solitons
Abstract
In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and L1 and L2 energy for drifting heat equation on closed manifolds with weighted measure. In some sense, this study is about the eigenvalue estimate on Ricci solitons.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations