A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ

Wu, Jie

doi:10.1090/proc/16875

A note on new weighted geometric inequalities for hypersurfaces in $\mathbb {R}^n$
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by Jie Wu;

Proc. Amer. Math. Soc. 152 (2024), 4049-4056

DOI: https://doi.org/10.1090/proc/16875

Published electronically: July 17, 2024

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Abstract:

In this note, we prove a family of sharp weighed inequalities which involve weighted $k$-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in $\mathbb {R}^n$. 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.

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Proceedings of the American Mathematical Society

A note on new weighted geometric inequalities for hypersurfaces in $\mathbb {R}^n$
HTML articles powered by AMS MathViewer

Abstract: