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Ancient Caloric Functions on Pseudohermitian Manifolds

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Abstract

For any Riemannian manifold with polynomial volume growth, Colding and Minicozzi obtained a sharp bound on the dimension of the space of ancient caloric functions with polynomial growth. For any pseudohermitian manifold satisfies doubling volume property and parabolic mean value property, we obtain in this paper a sharp bound on the dimension of the space of ancient pseudohermitian caloric functions with polynomial growth.

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Acknowledgements

The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Nos. 2020R1A6A1A03047877 and 2019R1F1A1041021), and by Korea Institute for Advanced Study (KIAS) grant funded by the Korea government (MSIP).

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  1. Department of Mathematics, Sogang University, Seoul, 04107, South Korea

    Pak Tung Ho

  2. Korea Institute for Advanced Study, Seoul, 02455, South Korea

    Pak Tung Ho

  3. Department of Mathematics, Tamkang University, Tamsui, New Taipei City, 251301, Taiwan

    Pak Tung Ho

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Ho, P.T. Ancient Caloric Functions on Pseudohermitian Manifolds. J Geom Anal 33, 41 (2023). https://doi.org/10.1007/s12220-022-01101-z

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  • DOI: https://doi.org/10.1007/s12220-022-01101-z

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