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Register a new userLocal Li-Yaus estimates on $RCD^*(K,N)$ metric measure spaces
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In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yaus estimate for weak solutions of the heat equation and prove a sharp Yaus gradient gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition $RCD^*(K,N).$
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In this paper, we will prove the Weyls law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.
In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yaus gradient estimate for harmonic functions is also obtained on Alexandrov spaces.
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