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

2024/06/25 by Julin, Vesa, Morini, Massimiliano, Oronzio, Francesca +1 · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.17691

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 C²-regular sets with a perimeter bound.

Cited by

• Flat flows of periodic Lipschitz subgraphs for generalized nonlocal perimeters
• Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane

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