The bridge principle for stable minimal surfaces

DOI10.1007/BF01192091zbMath0830.49025WikidataQ125772555 ScholiaQ125772555MaRDI QIDQ1344087

Brian White

Publication date: 18 January 1996

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifoldsminimal surfacesPlateau's problembridge principleblow up limitsparametric elliptic integralsstable smooth minimal submanifolds

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)

Related Items (4)

Non-uniqueness of minimizers for strictly polyconvex functionals ⋮ Existence of proper minimal surfaces of arbitrary topological type ⋮ \(H\)-surfaces with arbitrary topology in hyperbolic 3-space ⋮ Helicoidal minimal surfaces of prescribed genus

Cites Work

• Approximation by positive mean curvature immersions: frizzing
• Two topological examples in minimal surface theory
• A bridge principle for minimal and constant mean curvature submanifolds of \(R^ N\)
• The existence of embedded minimal surfaces and the problem of uniqueness
• Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds
• On the first variation of a varifold: Boundary behavior
• Soap films bounded by non-closed curves
• The bridge principle for unstable and for singular minimal surfaces
• Concerning the isolated character of solutions of Plateau's problem
• On the first variation of a varifold
• The geometry of the slice-ribbon problem
• A strong minimax property of nondegenerate minimal submanifolds.
• The bridge theorem for minimal surfaces
• The axiom of choice
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