Nonhomogeneous inverse Gauss curvature flow in $\mathbb {H}^{3}$
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- by Haizhong Li and Tailong Zhou PDF
- Proc. Amer. Math. Soc. 147 (2019), 3995-4005 Request permission
Abstract:
In this paper, we consider nonhomogeneous inverse Gauss curvature flows in hyperbolic space $\mathbb {H}^{3}$. We prove that if the initial hypersurface $\Sigma _0$ has nonnegative scalar curvature, then the evolving surface $\Sigma _{t}$ has nonnegative scalar curvature along the flow for $t>0$. The solution of the flow exists for all time and becomes more and more umbilic as $t\rightarrow \infty$.References
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Additional Information
- Haizhong Li
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
- MR Author ID: 255846
- Email: hli@math.tsinghua.edu.cn
- Tailong Zhou
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
- Email: zhou-tl14@mails.tsinghua.edu.cn
- Received by editor(s): October 10, 2018
- Received by editor(s) in revised form: January 6, 2019
- Published electronically: April 18, 2019
- Additional Notes: This research was supported by NSFC grant No.11671224 and NSFC grant No.11831005
- Communicated by: Guofang Wei
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3995-4005
- MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/proc/14549
- MathSciNet review: 3993791