Optimal transportation and monotonic quantities on evolving manifolds

2009/08/23 by Hong Huang, Huang, Hong
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR) #math.DG #math.PR #msc:53C44

paper · pdf · doi:10.48550/arxiv.0908.3293

8 pages, some corrections and extensions

arxiv created 2009/09/14 · arxiv updated 2009/12/01

Abstract

In this note we will adapt Topping's L-optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold (M,g_ij(t)) evolving by ∂_tg_ij=-2S_ij, where S_ij is a symmetric tensor field of (2,0)-type on M. We extend some recent results of Topping, Lott and Brendle, generalize the monotonicity of List's (and hence also of Perelman's) W-entropy, and recover the monotonicity of Muller's (and hence also of Perelman's) reduced volume.

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