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Bishop and Laplacian Comparison Theorems on Three-Dimensional Contact Sub-Riemannian Manifolds with Symmetry

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Abstract

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three-dimensional contact sub-Riemannian manifolds with symmetry.

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Acknowledgements

The authors would like to thank N. Garofalo for stimulating discussions.

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Authors and Affiliations

  1. International School for Advanced Studies, via Bonomea 265, 34136, Trieste, Italy

    Andrei Agrachev

  2. Steklov Mathematical Institute, ul. Gubkina 8, Moscow, 119991, Russia

    Andrei Agrachev

  3. The Chinese University of Hong Kong, Room 216, Lady Shaw Building, Shatin, Hong Kong

    Paul W. Y. Lee

Authors
  1. Andrei Agrachev
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  2. Paul W. Y. Lee
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Corresponding author

Correspondence to Paul W. Y. Lee.

Additional information

Communicated by Der-Chen Edward Chang.

The first author was partially supported by the PRIN project and the second author was supported by the NSERC postdoctoral fellowship.

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Agrachev, A., Lee, P.W.Y. Bishop and Laplacian Comparison Theorems on Three-Dimensional Contact Sub-Riemannian Manifolds with Symmetry. J Geom Anal 25, 512–535 (2015). https://doi.org/10.1007/s12220-013-9437-2

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  • DOI: https://doi.org/10.1007/s12220-013-9437-2

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