## Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball

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- by Liangjun Weng and Chao Xia PDF
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## Abstract:

In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball ${\mathbb {B}}^{n+1}$ and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the $n$-th quermassintegral and non-decreases the $k$-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in ${\mathbb {B}}^{n+1}$. This generalizes the result of Scheuer [J. Differential Geom. 120 (2022), pp. 345–373] for convex hypersurfaces with free boundary in ${\mathbb {B}}^{n+1}$.## References

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## Additional Information

**Liangjun Weng**- Affiliation: School of Mathematical Sciences, Anhui University, Hefei 230601, People’s Republic of China
- MR Author ID: 1314718
- Email: ljweng08@mail.ustc.edu.cn
**Chao Xia**- Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
- MR Author ID: 922365
- Email: chaoxia@xmu.edu.cn
- Received by editor(s): November 10, 2021
- Received by editor(s) in revised form: May 29, 2022, May 31, 2022, and June 1, 2022
- Published electronically: October 3, 2022
- Additional Notes: Chao Xia is the corresponding author

The first author was supported by project funded by China Postdoctoral Science Foundation (No. 2021M702143) and NSFC (Grant No. 12171260). The second author was supported by NSFC (Grant No. 11871406). Parts of this work were done while the first author was visiting the Tianyuan Mathematical Center in Southeast China and school of mathematical sciences at Xiamen University under the support of NSFC (Grant No. 12126102) - © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 8851-8883 - MSC (2020): Primary 53C21, 35K96, 52A40
- DOI: https://doi.org/10.1090/tran/8756