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Uniform Sobolev Inequality along the Sasaki–Ricci Flow

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Abstract

In this paper we prove a uniform Sobolev inequality along the Sasaki–Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold.

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Acknowledgements

I would like to thank my advisor Professor D.H. Phong for his guidance and encouragement, as well as for suggesting this problem. I would also like to thank Professors Valentino Tosatti and Gabor Székelyhidi for many helpful suggestions during the writing of this paper. I am also grateful to the referee for pointing out several typos in a previous version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Tristan C. Collins

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  1. Tristan C. Collins
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Correspondence to Tristan C. Collins.

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Communicated by Jiaping Wang.

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Collins, T.C. Uniform Sobolev Inequality along the Sasaki–Ricci Flow. J Geom Anal 24, 1323–1336 (2014). https://doi.org/10.1007/s12220-012-9374-5

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  • DOI: https://doi.org/10.1007/s12220-012-9374-5

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