Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds

2011/05/05 by Shin‐ichi Ohta, Ohta, Shin-ichi, Karl‐Theodor Sturm +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1105.0983

openalex publication_date 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ricci curvature for metric-measure spaces via optimal transport

Cited by

• On the Equivalence of the Entropic Curvature-Dimension Condition and\n Bochner's Inequality on Metric Measure Spaces
• Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter
• Displacement convexity of generalized relative entropies

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