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Received May 28, 2017; Accepted November 2, 2017; Published November 9, 2017
Abstract. In this paper, we establish heat kernel upper bounds via ultracontractive estimates for heat diffusion semigroups on an n-dimensional complete Riemannian manifold M. This result is extended, via monotonicity property of the W-entropy functional, to the case when M is stochastically complete. We also prove the large time asymptotic of the entropy for the stochastic complete heat kernel. This provides an alternative proof for Ni’s large time asymptotic of the entropy.
How to Cite this Article:
Abimbola Abolarinwa, Heat kernel estimates and asymptotic of W-entropy on stochastically complete Riemannian manifolds, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 51, pp. 1-14.