Heat flow on Finsler manifolds

Details Heat flow on Finsler manifolds Heat flow on Finsler manifolds

2008-08-08

arxiv.org/abs/0808.1166v3

Comm. Pure. Appl. Math. 62 (2009), 1386-1433

Mathematics

Analysis of PDEs

36 pages (without figures); v3: minor changes, to appear in Comm. Pure Appl. Math

Scientific paper

We present two approaches to the heat flow on a Finsler manifold $(M,F)$: either as gradient flow on $L^2(M,m)$ for the energy; or as gradient flow on the reverse $L^2$-Wasserstein space $\mathcal{P}_2(M)$ of probability measures on $M$ for the relative entropy. Both approaches depend on the choice of a measure $m$ on $M$ and then lead to the same nonlinear evolution semigroup. We prove $\mathcal{C}^{1,\alpha}$-regularity for solutions to the (nonlinear) heat equation on the Finsler space $(M,F,m)$. Typically, solutions to the heat equation will not be $\mathcal{C}^2$. Moreover, we derive pointwise comparison results a la Cheeger-Yau and integrated upper Gaussian estimates a la Davies.

Affiliated with

Also associated with

No associations

Rating

Heat flow on Finsler manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Heat flow on Finsler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heat flow on Finsler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-29377