Non-contraction of heat flow on Minkowski spaces

Details Non-contraction of heat flow on Minkowski spaces Non-contraction of heat flow on Minkowski spaces

2010-09-13

arxiv.org/abs/1009.2312v4

Mathematics

Analysis of PDEs

26 pages; minor revisions, to appear in Arch. Ration. Mech. Anal

Scientific paper

We study contractivity properties of gradient flows for functions on normed spaces or, more generally, on Finsler manifolds. Contractivity of the flows turns out to be equivalent to a new notion of convexity for the functions. This is different from the usual convexity along geodesics in non-Riemannian Finsler manifolds. As an application, we show that the heat flow on Minkowski normed spaces other than inner product spaces is not contractive with respect to the quadratic Wasserstein distance.

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