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Sharp Davies–Gaffney–Grigor’yan Lemma on graphs

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Abstract

In this note, we prove the sharp Davies–Gaffney–Grigor’yan Lemma for minimal heat kernels on graphs.

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Acknowledgements

We thank Alexander Grigor’yan, Thierry Coulhon and Adam Sikora for many fruitful discussions on Davies–Gaffney–Grigor’yan Lemma on manifolds and metric measure spaces, and thank the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Frank Bauer & Shing-Tung Yau

  2. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    Frank Bauer

  3. School of Mathematical Sciences, LMNS, Fudan University, Shanghai, 200433, China

    Bobo Hua

  4. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Bobo Hua

Authors
  1. Frank Bauer
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  2. Bobo Hua
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  3. Shing-Tung Yau
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Corresponding author

Correspondence to Bobo Hua.

Additional information

Communicated by Thomas Schick.

F.B. was partially supported by the Alexander von Humboldt foundation. S.T.Y. acknowledges support by the University of Pennsylvania/Air Force Office of Scientific Research grant “Geometry and Topology of Complex Networks”, Award #561009/FA9550-13-1-0097 and NSF DMS 1308244 Nonlinear Analysis on Sympletic, Complex Manifolds, General Relativity, and graph. B.H. was supported by NSFC, Grant no. 11401106.

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Bauer, F., Hua, B. & Yau, ST. Sharp Davies–Gaffney–Grigor’yan Lemma on graphs. Math. Ann. 368, 1429–1437 (2017). https://doi.org/10.1007/s00208-017-1529-z

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  • DOI: https://doi.org/10.1007/s00208-017-1529-z

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