关于总平均曲率和面积约束下Willmore能量的最小化

IF 2.4 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2025-02-13 DOI:10.1007/s00205-025-02087-y

Christian Scharrer, Alexander West

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引用次数: 0

摘要

在脂质双层细胞膜模型的激励下，我们研究了具有规定的总平均曲率、规定的面积和规定的属的定向封闭表面类中Willmore泛函的最小化。采用先前由keller - mon迪诺- rivi， Bauer-Kuwert和Ndiaye-Schätzle开发的方法，我们证明了一类约束的光滑最小化的存在性。此外，我们分析了能量分布在单位球附近的渐近行为，并考虑了轴对称曲面的总平均曲率。

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On the Minimization of the Willmore Energy Under a Constraint on Total Mean Curvature and Area

Motivated by a model for lipid bilayer cell membranes, we study the minimization of the Willmore functional in the class of oriented closed surfaces with prescribed total mean curvature, prescribed area, and prescribed genus. Adapting methods previously developed by Keller–Mondino–Rivière, Bauer–Kuwert, and Ndiaye–Schätzle, we prove the existence of smooth minimizers for a large class of constraints. Moreover, we analyze the asymptotic behaviour of the energy profile close to the unit sphere and consider the total mean curvature of axisymmetric surfaces.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.