Uniqueness theorems of self-conformal solutions to inverse curvature flows
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- by Nicholas Cheng-Hoong Chin, Frederick Tsz-Ho Fong and Jingbo Wan
- Proc. Amer. Math. Soc. 148 (2020), 4967-4982
- DOI: https://doi.org/10.1090/proc/15163
- Published electronically: August 17, 2020
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Abstract:
It is known from the literature that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree $-1$ homogeneous functions of principal curvatures in the Euclidean space.
In this article, we prove that the round sphere is rigid in a stronger sense: under some natural conditions such as star-shapedness, round spheres are the only closed solutions to the above-mentioned flows which evolve by diffeomorphisms generated by conformal Killing fields.
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Bibliographic Information
- Nicholas Cheng-Hoong Chin
- Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Email: nchchin@connect.ust.hk
- Frederick Tsz-Ho Fong
- Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- MR Author ID: 891635
- Email: frederick.fong@ust.hk
- Jingbo Wan
- Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Email: jwanac@connect.ust.hk
- Received by editor(s): December 19, 2019
- Received by editor(s) in revised form: April 17, 2020
- Published electronically: August 17, 2020
- Additional Notes: The first author was partially supported by the HKUST postgraduate studentship.
The research conducted was partially supported by the second author’s Hong Kong RGC Early Career Grant #26301316 and General Research Fund #16302417.
The third author was partially supported by the HKUST Undergraduate Research Opportunity Project (UROP). - Communicated by: Jia-Ping Wang
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4967-4982
- MSC (2020): Primary 53E10
- DOI: https://doi.org/10.1090/proc/15163
- MathSciNet review: 4143407