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. 2025;249(6):78.
doi: 10.1007/s00205-025-02141-9. Epub 2025 Nov 21.

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

Vesa Julin  1 , Massimiliano Morini  2 , Francesca Oronzio  3 , Emanuele Spadaro  4
Affiliations

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

Vesa Julin et al. Arch Ration Mech Anal. 2025.

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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Conflict of interest statement

Conflict of interestThe authors have no Conflict of interest to declare that are relevant to the content of this article.

References

    1. Acerbi, E., Fusco, N., Morini, M.: Minimality via second variation for a nonlocal isoperimetric problem. Comm. Math. Phys.322, 515–557, 2013
    1. Alikakos, N.D., Bates, P.W., Chen, X.: Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Arch. Ration. Mech. Anal.128, 165–205, 1994
    1. Almgren, F., Taylor, J., Wang, L.: Curvature-driven flows: a variational approach. SIAM J. Control Optim.31, 387–438, 1993
    1. Bauer, M., Kuwert, E.: Existence of minimizing Willmore surfaces of prescribed genus. Int. Math. Res. Not.2003, 553–576, 2003
    1. Benedetti, R.: Lectures on Differential Topology. Graduate Studies in Mathematics. American Mathematical Society, Providence, 2021

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