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【期刊论文】SHARP EXPLICIT LOWER BOUNDS OF HEAT KERNELS1
王凤雨, By Feng-Yu Wang
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-1年11月30日
By using logarithmic transformations, an explicit lower bound estimate of heat kernels is obtained for diffusion processes on Riemannian manifolds. This estimate is sharp for both short and long times, especially for heat kernels on a compact manifold, and is extended to manifolds with unbounded curvature.
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【期刊论文】CHEEGER'S INEQUALITIES FOR GENERAL SYMMETRIC FORMS AND EXISTENCE CRITERIA FOR SPECTRAL GAP
王凤雨, Mu-Fa Chen and Feng-Yu Wang
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-1年11月30日
In this paper, some new forms of the Cheeger’s inequalities are established for general (maybe unbounded) symmetric forms (Theorem 1.1 and Theorem 1.2), the resulting estimates improve and extend the ones obtained by Lawler and Sokal (1988) for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented (Theorem 1.4 and Theorem 3.1), based on the Cheeger’s inequalities and a relationship between the spectral gap and the first Dirichlet and Neumann eigenvalues on local region.
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