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Title: Willmore energy of conformal immersions
Authors: Kuan, Jeffrey
Advisors: Chang, Alice
Yang, Paul
Department: Mathematics
Class Year: 2018
Abstract: In this thesis, we summarize a result by Kuwert and Li [1] about the minimizers of the Willmore energy among the class of conformal immersions f : S^2 → R^3 with fixed isoperimetric ratio \sigma. Using results by Schygulla [2] as a starting point, we follow Kuwert and Li’s argument in [1] about the behavior of these minimizers as the isoperimetric ratio \sigma tends to zero. To do this, we first present some basic facts about conformal immersions, and then introduce some results by Chen and Li [3] about bubbles, concentration points, and the bubble tree. Then, we present the argument by Kuwert and Li [1] about the limiting behavior of the Willmore minimizers as the isoperimetric ratio \sigma goes to zero.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

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