Bochner-Weitzenb\"ock formula and Li-Yau estimates on Finsler manifolds
By Shin-ichi Ohta, Karl‐Theodor Sturm. 2011
133 citations recorded by the source corpus.
We prove the Bochner-Weitzenb\"ock 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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e207a6548ac8b4547f594a23554c568c00c5512c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Andrea Mondino
- Fabio Cavalletti
- Shin-ichi Ohta
- Nicola Gigli
- Guofang Wang
- Karl‐Theodor Sturm
- Emanuel Milman
- Chao Xia
In Astronomy and Astrophysics
- Andrea Mondino
- Fabio Cavalletti
- Karl‐Theodor Sturm
- Shin-ichi Ohta
- Chao Xia
- Guofang Wang
- Nicola Gigli
- Luigi Ambrosio
In Geometry and Topology
- Andrea Mondino
- Fabio Cavalletti
- Shin-ichi Ohta
- Nicola Gigli
- Chao Xia
- Guofang Wang
- Emanuel Milman
- Karl‐Theodor Sturm
Citations in the corpus
- An optimal anisotropic Poincaré inequality for convex domains (2011, methodology): “hen F(ξ) = |ξ| = ( Pn i=1 |ξi| 2)1/2, the Finsler-Laplacian Q= ∆, the usual Laplacian. The Finsler-Laplacian has been studied by many mathematicians, both in the context of Finsler geometry (see e.g. [1, 7, 14, 15, 18]) and quasilinear PDE ( see e.g. [2, 4, 8, 20, 21, 22]). Especially, many problems”
- New formulas for the Laplacian of distance functions and applications (2018, background): “linearity of the heat flow was a crucial assumption in all of the aforementioned works. The equivalence between Bochner inequality and CD(K,N) was proved also in smooth Finsler manifolds by Ohta-Sturm [49]. In [49] no linearity of the heat flow is assumed, on the other hand the smoothness of the Finsl”
- Non-Contraction of Heat Flow on Minkowski Spaces (2010, methodology): “nifolds. Among other characterizations of lower Ricci curvature 2 bounds for Riemannian manifolds, we recently verified that the Bochner-Weitzenb¨ock formula makes sense for general Finsler manifolds ([OS2]). The article is organized as follows. After preliminaries for Minkowski and Finsler geometrie”