A two-point function approach to connectedness of drops in convex potentials
A two-point function approach to connectedness of drops in convex potentials
复制标题
凸势中液滴连通性的两点函数方法
DOI：
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发表时间：
2018
影响因子：
0.7
通讯作者：
G. Philippis
中科院分区：
文献类型：
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作者：
M. Goldman;G. Philippis
我们建立了涉及表面张力和凸势的体积约束能量极小值的连通性。根据McCann以前的结果，这意味着极小化在二维凸性。这肯定地回答了阿尔姆格伦的一个老问题。我们还证明了当放弃体积约束时极小值的凸性。我们的证明是基于引入了一个新的“两点函数”，它测量了凸性的缺乏，并引起了能量的负二次变化。
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an old question of Almgren. We also prove convexity of minimisers when the volume constraint is dropped. Our proof is based on the introduction of a new " two-point function " which measures the lack of convexity and which gives rise to a negative second variation of the energy.