An a priori estimate for the oscillation of the normal to a hypersurface whose first and second variation with respect to an elliptic integrand is controlled

DOI10.1007/BF01394028zbMath0526.49028MaRDI QIDQ595185

William K. Allard

Publication date: 1983

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143048

zbMATH Keywords

stable minimal hypersurfaceelliptic integrandfirst and second variation, a priori estimate

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

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Cites Work

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• Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
• On the first variation of a varifold
• On the First and Second Variation of a Parametric Integral
• Regularity of stable minimal hypersurfaces
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

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