Function theory and index for minimal surfaces of genus 1. I: Fredholm bundles of holomorphic functions on punched tori

DOI10.1007/BF01195359zbMath0601.58057OpenAlexW231294788WikidataQ122803057 ScholiaQ122803057MaRDI QIDQ1081175

Karl-Heinz Schüffler

Publication date: 1987

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01195359

zbMATH Keywords

Riemann-Hilbert problemTeichmüller spaceplateau problemdouble periodic functionsconformal types of the torifunction theoretical aspects of the minimal surface theoryindextheorysurfaces of higher genustopological and conformal structurevariation of conformal structures

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Exotic index theories on manifolds (58J22) Holomorphic bundles and generalizations (32L05)

Related Items (3)

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 ⋮ Zur Fredholmtheorie des Riemann-Hilbert-Operators. (Fredholm theory of the Riemann-Hilbert operator)

Cites Work

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• Plateau's problem for surfaces of constant mean curvature from a global point of view
• Zur Fredholmtheorie des Riemann-Hilbert-Operators. (Fredholm theory of the Riemann-Hilbert operator)
• Eine globalanalytische Behandlung des Douglas'schen Problems. (A global analysis treatment of the Douglas problem)
• A classification problem for Riemann surfaces of genus 1.
• Stabilität mehrfach zusammenhängender Minimalflächen
• The index theorem for classical minimal surfaces
• Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung
• The Riemann-Hilbert problem for finite riemann surfaces
• On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
• On the number of simply connected minimal surfaces spanning a curve

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