On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.

DOI10.1515/crll.1980.316.31zbMath0421.58002OpenAlexW4251334808MaRDI QIDQ3854335

Anthony J. Tromba, Friedrich Tomi

Publication date: 1980

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002197294

zbMATH Keywords

Fredholm mapBanach manifoldsconnectivity propertiescurves bounding minimal surfacesdegree theory for Plateau's problemFredholm index theorem for branched minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Spaces of embeddings and immersions (58D10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Differentiable maps on manifolds (58C25) Homotopy and topological questions for infinite-dimensional manifolds (58B05)

Related Items (8)

Function theory and index for minimal surfaces of genus 1. I: Fredholm bundles of holomorphic functions on punched tori ⋮ Function theory and index theory for minimal surfaces of genus 1. II. Manifold structures for double periodic minimal surfaces ⋮ Function theory and index theory for minimal surfaces of genus 1. III: The index theorem for minimal surfaces of genus 1 ⋮ Eine globalanalytische Behandlung des Douglas'schen Problems. (A global analysis treatment of the Douglas problem) ⋮ Ein Indexsatz für Flächen konstanter mittlerer Krümmung ⋮ On the nonexistence of boundary branch points for minimal surfaces spanning smooth contours. II ⋮ Plateau's problem for surfaces of constant mean curvature from a global point of view ⋮ On the Morse number of embedded and non-embedded minimal immersions spanning wires on the boundary of special bodies in \({\mathbb{R}}^ 3\)

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