Asymptotics of Willmore Minimizers with Prescribed Small Isoperimetric Ratio
Asymptotics of Willmore Minimizers with Prescribed Small Isoperimetric Ratio
复制标题
具有规定小等周比的 Willmore 极小化的渐近
DOI：
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发表时间：
2017
影响因子：
2
通讯作者：
Yuxiang Li
中科院分区：
文献类型：
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作者：
E. Kuwert;Yuxiang Li
我们考虑${mathbb S}^2$中的曲面，它使Willmore泛函在给定的等周比下最小化。Schygulla（Archive Rational Mechanics and Analysis，2012）证明了光滑极小点的存在性。在奇异极限时的等周比收敛到零，他表明收敛到一个双圆球的意义上varifolds。在这里，我们给出了一个完整的爆破分析，这一限制，表明这两个领域是由悬链颈连接。除了其几何意义外，该问题还作为细胞膜理论中的简化模型进行了研究，参见Berndl，Lipowsky，Seifert（Physical Review A，1991）。
We consider surfaces in ${mathbb R}^3$ of type ${mathbb S}^2$ which minimize the Willmore functional with prescribed isoperimetric ratio. The existence of smooth minimizers was proved by Schygulla (Archive Rational Mechanics and Analysis, 2012). In the singular limit when the isoperimetric ratio converges to zero, he showed convergence to a double round sphere in the sense of varifolds. Here we give a full blowup analysis of this limit, showing that the two spheres are connected by a catenoidal neck. Besides its geometric interest, the problem was studied as a simplified model in the theory of cell membranes, see e.g. Berndl, Lipowsky, Seifert (Physical Review A, 1991).
具有指定等周比的 Willmore 最小化器
影响因子：
2.5
作者：
Schygulla
通讯作者：
Schygulla