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Yamabe solitons with boundary

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Abstract

Yamabe soliton is a self-similar solution to the Yamabe flow on manifolds without boundary. In this paper, we define and study the Yamabe soliton with boundary and conformal mean curvature soliton, which are natural generalizations of the Yamabe soliton. We study these solitons from equation point of view. We also study their two-dimensional analog: the Gauss curvature soliton with boundary and geodesic curvature soliton.

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Acknowledgements

We would like to thank the anonymous referee for his/her very careful reading of the manuscript and his/her many insightful comments and suggestions. The second author was supported by a KIAS Individual Grant (MG070701) at Korea Institute for Advanced Study.

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Authors and Affiliations

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

    Pak Tung Ho

  2. Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Korea

    Jinwoo Shin

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  1. Pak Tung Ho
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  2. Jinwoo Shin
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Correspondence to Pak Tung Ho.

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Ho, P.T., Shin, J. Yamabe solitons with boundary. Annali di Matematica 202, 2219–2253 (2023). https://doi.org/10.1007/s10231-023-01318-x

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