Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary

DOI10.1090/S0002-9939-2014-12351-3zbMath1314.53113arXiv1302.4165OpenAlexW1982554483WikidataQ115289239 ScholiaQ115289239MaRDI QIDQ5179339

Glen Wheeler

Publication date: 19 March 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4165

zbMATH Keywords

uniqueness theoremsurface diffusionWillmore surfacesbiharmonic submanifoldsgap phenomena

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometric aspects of harmonic maps (53C43) Higher-order elliptic equations (35J30)

Related Items (6)

The geometric triharmonic heat flow of immersed surfaces near spheres ⋮ An energy gap phenomenon for the Whitney sphere ⋮ Willmore flow of complete surfaces ⋮ Energy estimates for the tracefree curvature of Willmore surfaces and applications ⋮ Analysis of the inhomogeneous Willmore equation ⋮ A rigidity theorem for ideal surfaces with flat boundary

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• Extrinsic rigidity theorems for compact submanifolds of the sphere
• Uniqueness theorems for Willmore surfaces with fixed and free boundaries
• Linearized stability analysis of surface diffusion for hypersurfaces with boundary contact
• Submanifolds with Constant Mean Curvature
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

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