## A class of curvature flows expanded by support function and curvature function

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- by Shanwei Ding and Guanghan Li PDF
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## Abstract:

In this paper, we consider a class of expanding flows of closed, smooth, uniformly convex hypersurfaces in Euclidean $\mathbb {R}^{n+1}$ with speed $u^\alpha f^\beta$ ($\alpha , \beta \in \mathbb {R}^1$), where $u$ is the support function of the hypersurface, $f$ is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If $\alpha \leqslant 0<\beta \leqslant 1-\alpha$, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin.## References

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## Additional Information

**Shanwei Ding**- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
- ORCID: 0000-0002-8383-5219
**Guanghan Li**- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
- Received by editor(s): March 20, 2020
- Received by editor(s) in revised form: May 14, 2020
- Published electronically: September 18, 2020
- Additional Notes: This research was partially supported by NSFC (Nos. 11761080 and 11871053).
- Communicated by: Jia-Ping Wang
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5331-5341 - MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/proc/15189
- MathSciNet review: 4163845