Renjin Jiang

activity

20092026

most citedHamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

11 citations · 56 across the 24 of their papers we have counts for

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5 papers · 1 filter

math.MG2017

Gradient estimates for heat kernels and harmonic functions

Thierry Coulhon, Renjin Jiang, Pekka Koskela +1

Let $(X, d, μ)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carré du champ". Assume that $(X,d,μ,\E)$ supports a scale-invariant $L^{2}$ -Poin…

math.MG2015★ 11 cited

Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

Renjin Jiang, Huichun Zhang

In this paper, we extend the Hamilton's gradient estimates \cite{har93} and a monotonicity formula of entropy \cite{ni04} for heat flows from smooth Riemannian manifolds to (non-sm…

math.MG2014★ 7 cited

Heat Kernel Bounds on Metric Measure Spaces and Some Applications

Renjin Jiang, Huaiqian Li, Huichun Zhang

Let $(X, d, μ)$ be a $R C D^{*} (K, N)$ space with $K \in R$ and $N \in [1, \infty]$ . For $N \in [1, \infty)$ , we derive the upper and lower bounds of the heat kernel on $(X, d, μ)$ …

math.MG2014★ 3 cited

The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Renjin Jiang

Let $(X, d, μ)$ be a $R C D^{*} (K, N)$ space with $K \in ma t hbb R$ and $N \in [1, \infty)$ . Suppose that $(X, d)$ is connected, complete and separable, and $\supp μ=X$. We prove that the…

math.MG2013★ 5 cited

Cheeger-harmonic functions in metric measure spaces revisited

Renjin Jiang

Let $(X, d, μ)$ be a complete metric measure space, with $μ$ a locally doubling measure, that supports a local weak $L^{2}$ -Poincaré inequality. By assuming a heat semigroup type curva…