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|Title:||Willmore energy of conformal immersions|
|Abstract:||In this thesis, we summarize a result by Kuwert and Li  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  as a starting point, we follow Kuwert and Li’s argument in  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  about bubbles, concentration points, and the bubble tree. Then, we present the argument by Kuwert and Li  about the limiting behavior of the Willmore minimizers as the isoperimetric ratio \sigma goes to zero.|
|Type of Material:||Princeton University Senior Theses|
|Appears in Collections:||Mathematics, 1934-2020|
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