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Local Li–Yau’s estimates on RCD \(^*(K,N)\) metric measure spaces

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Abstract

In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li–Yau’s estimate for weak solutions of the heat equation and prove a sharp Yau’s gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition RCD \(^*(K,N)\).

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Acknowledgments

H. C. Zhang is partially supported by NSFC 11571374. X. P. Zhu is partially supported by NSFC 11521101.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Hui-Chun Zhang & Xi-Ping Zhu

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  1. Hui-Chun Zhang
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  2. Xi-Ping Zhu
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Correspondence to Hui-Chun Zhang.

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Communicated by L. Ambrosio.

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Zhang, HC., Zhu, XP. Local Li–Yau’s estimates on RCD \(^*(K,N)\) metric measure spaces. Calc. Var. 55, 93 (2016). https://doi.org/10.1007/s00526-016-1040-5

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