Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds
Shin-ichi Ohta, Karl-Theodor Sturm
TL;DR
This paper extends fundamental geometric analysis tools to Finsler manifolds, establishing a Bochner-Weitzenboeck formula, Li-Yau estimates, and Harnack inequalities, all depending on Ricci curvature bounds.
Contribution
It introduces a Bochner-Weitzenboeck formula for the nonlinear Laplacian on Finsler manifolds and derives key gradient and Harnack estimates.
Findings
Established a Bochner-Weitzenboeck formula for Finsler manifolds
Derived Li-Yau gradient estimates and Harnack inequalities
Connected estimates to lower bounds of weighted flag Ricci tensor
Abstract
We prove the Bochner-Weitzenboeck formula for the (nonlinear) Laplacian on general Finsler manifolds and derive Li-Yau type gradient estimates as well as parabolic Harnack inequalities. Moreover, we deduce Bakry-Emery gradient estimates. All these estimates depend on lower bounds for the weighted flag Ricci tensor.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Geometry and complex manifolds