JournalsaihpcVol. 41, No. 1pp. 129–158

Analysis of the inhomogeneous Willmore equation

  • Yann Bernard

    Monash University, Victoria, Australia

  • Glen Wheeler

    University of Wollongong, New South Wales, Australia

  • Valentina-Mira Wheeler

    University of Wollongong, New South Wales, Australia
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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 bi-harmonic surfaces in the sense of Chen, among others. We prove several local energy estimates and derive a global gap lemma.

Cite this article

Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler, Analysis of the inhomogeneous Willmore equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 1, pp. 129–158

DOI 10.4171/AIHPC/79