A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ-Reference-Cited by-同舟云学术

A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ

Published:2024-07-17 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Wu Jie

Abstract

In this note, we prove a family of sharp weighed inequalities which involve weighted k k -th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in R n \mathbb {R}^n . This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao’s results.

Funder

National Key Research and Development Program of China

Publisher

American Mathematical Society (AMS)

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2024-16875-1/proc16875_AM.pdf

Reference15 articles.

1. A.D. Alexandrov, Zur Theorie der gemischten Volumina von konvexen Körpern, II. Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen, Mat. Sb. (N.S.) 2 (1937) 1205–1238 (in Russian).

2. A.D. Alexandrov, Zur Theorie der gemischten Volumina von konvexen Körpern, III. Die Erweiterung zweeier Lehrsatze Minkowskis über die konvexen Polyeder auf beliebige konvexe Flachen, Mat. Sb. (N.S.) 3 (1938) 27–46 (in Russian).

3. Stability of hypersurfaces with constant 𝑟-mean curvature;Barbosa, João Lucas Marques;Ann. Global Anal. Geom.,1997

4. Weighted geometric inequalities for hypersurfaces in sub-static manifolds;Girão, Frederico;Bull. Lond. Math. Soc.,2020

5. Flow of nonconvex hypersurfaces into spheres;Gerhardt, Claus;J. Differential Geom.,1990