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Uniform gradient estimates on manifolds with a boundary and applications

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Abstract

We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperimetric inequalities, using Ledoux’s argument, and uniform quantitative gradient estimates, firstly for \(C^2_b\) functions with boundary conditions and then for the unit spectral projection operators of Dirichlet and Neumann Laplacians.

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Acknowledgements

This work has been supported by the Fonds National de la Recherche Luxembourg (FNR) under the OPEN scheme (Project GEOMREV O14/7628746). The first named author acknowledges support by NSFC (Grant No. 11501508) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ16A010009).

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Authors and Affiliations

  1. Mathematics Research Unit, University of Luxembourg, Campus Belval, 4364, Esch-sur-Alzette, Luxembourg

    Li-Juan Cheng, Anton Thalmaier & James Thompson

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  1. Li-Juan Cheng
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  2. Anton Thalmaier
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  3. James Thompson
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Correspondence to Anton Thalmaier.

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All authors declare that they have no conflicts of interest.

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To the memory of Sasha Vasil’ev.

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Cheng, LJ., Thalmaier, A. & Thompson, J. Uniform gradient estimates on manifolds with a boundary and applications. Anal.Math.Phys. 8, 571–588 (2018). https://doi.org/10.1007/s13324-018-0228-6

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  • DOI: https://doi.org/10.1007/s13324-018-0228-6

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