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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-regular sets with a perimeter bound.</p>

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A Sharp Quantitative Alexandrov Inequality and Applications to Volume Preserving Geometric Flows in 3D

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月21日

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  • Vesa Julin,
  • Massimiliano Morini,
  • Francesca Oronzio,
  • Emanuele Spadaro

摘要

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 \(C^2\) C 2 -regular sets with a perimeter bound.