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arXiv · 2201.04256

Quantitative Quermassintegral Inequalities for Nearly Spherical Sets

Caroline VanBlargan·Yi Wang
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Abstract

In this paper, we establish quantitative Alexandrov-Fenchel inequalities for quermassintegrals on nearly spherical sets. In particular, we bound the $(k,m)$-isoperimetric deficit from below by the Frankael asymmetry. We also find a lower bound on the $(k,m)$-isoperimetric deficit using the spherical deviation.

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Caroline VanBlargan, Yi Wang. 2022-01-12. Quantitative Quermassintegral Inequalities for Nearly Spherical Sets. https://arxiv.org/abs/2201.04256

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