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摘要
We consider surfaces in R-3 of type S-2 which minimize the Willmore functional with prescribed isoperimetric ratio. In [Arch. Ration. Mech. Anal., 203 (2012), pp. 901-941] Schygulla proved the existence of smooth minimizers. 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 has been studied as a simplified model in the theory of cell membranes; see, e.g., [K. Berndl, R. Lipowsky, and U. Seifert, Phys. Rev. A, 44 (1991), pp. 1182-1202].
- 出版日期2018
- 单位清华大学
