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Gradient estimates of porous medium equations under the Ricci flow

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Abstract

In this paper we consider an n-dimensional manifold M n evolving under the Ricci flow and establish gradient estimates for positive solutions of porous medium equations on M n. As applications, we derive Harnack type inequalities. In particular, our results generalize gradient estimates for positive solutions of the heat equations in Liu (Pacific J Math 243:165–180 [18]).

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Authors and Affiliations

  1. Department of Mathematics, Henan Normal University, Xinxiang, 453007, P. R. China

    Bingqing Ma & Jing Li

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  1. Bingqing Ma
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  2. Jing Li
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Correspondence to Bingqing Ma.

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The research is supported by NSFC grant (No. 11171368, 11371018) and Henan Provincial Education department (No. 14B110017).

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Ma, B., Li, J. Gradient estimates of porous medium equations under the Ricci flow. J. Geom. 105, 313–325 (2014). https://doi.org/10.1007/s00022-013-0209-8

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  • DOI: https://doi.org/10.1007/s00022-013-0209-8

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