论文标题
严格的不平等，对于在等等约束下最小化Willmore功能
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
论文作者
论文摘要
受Kusner和Bauer-Kuwert的先前工作的启发，我们证明了两个表面的Willmore能量之间的严格不平等及其在等值约束的背景下的连接总和。在Keller-Mondino-Rivière先前的工作的基础上，我们严格的不平等会导致在每个属中存在等等限制的Willmore问题的最小值，前提是最小的能量严格在$8π$以下。除了几何兴趣之外，在文献中，在脂质双层细胞膜理论中已经研究了这种最小化问题。
Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperimetric constraints. Building on previous work by Keller-Mondino-Rivière, our strict inequality leads to existence of minimisers for the isoperimetric constrained Willmore problem in every genus, provided the minimal energy lies strictly below $8π$. Besides the geometric interest, such a minimisation problem has been studied in the literature as a simplified model in the theory of lipid bilayer cell membranes.
