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Analysis of the inhomogeneous Willmore equation

Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE（2024）

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Abstract
We study a class of fourth -order geometric problems modeling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, and biharmonic surfaces in the sense of Chen, among others. We prove several local energy estimates and derive a global gap lemma.
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Key words
Willmore,Helfrich,regularity,inhomogeneous
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