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Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures

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Abstract

By establishing the intrinsic super-Poincaré inequality, some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive. These conditions, as well as the resulting uniform upper bounds on the intrinsic heat kernels, are sharp for some concrete examples.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    FengYu Wang

  2. Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    FengYu Wang

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  1. FengYu Wang
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Correspondence to FengYu Wang.

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Wang, F. Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures. Sci. China Math. 53, 895–904 (2010). https://doi.org/10.1007/s11425-010-0019-5

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  • DOI: https://doi.org/10.1007/s11425-010-0019-5

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