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arXiv · 2406.17691

A sharp quantitative Alexandrov inequality and applications to volume preserving geometric flows in 3D

Vesa Julin·Massimiliano Morini·Francesca Oronzio·Emanuele Spadaro
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Abstract

We study the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flow in three dimensional space. Motivated by this we establish a 3D sharp quantitative version of the Alexandrov inequality for $C^2$-regular sets with a perimeter bound.

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Vesa Julin, Massimiliano Morini, Francesca Oronzio, Emanuele Spadaro. 2024-06-25. A sharp quantitative Alexandrov inequality and applications to volume preserving geometric flows in 3D. https://arxiv.org/abs/2406.17691

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