Analysis shows asymptotic behavior of geometric flows in 3D, indicating deep connections to Alexandrov inequality.
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 C 2 -regular sets with a perimeter bound.
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Julin et al. (2025) studied this question.
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