Titlebook: Global Analysis of Minimal Surfaces; Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb Book 1992Latest edition Springer-Verlag Berlin Hei

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Global Analysis of Minimal Surfaces978-3-642-11706-0Series ISSN 0072-7830 Series E-ISSN 2196-9701

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https://doi.org/10.1007/978-3-642-11706-049Q05,53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20; calculus of variations; conformal mappin

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Bernstein Theorems and Related Results .-dimensional minimal surface equation as well as for stationary points of singular integrals of the type ., called .-.. The basic results are . and . for minimal hypersurfaces. Essential tools are formulae for the first and second variation, Simons’s identity for the second fundamental form and “J

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The General Problem of Plateau: Another Approach curves .. may bound multiply connected minimal surfaces that could be of higher genus and even nonorientable; for a special case this problem was studied in Vol.?1. As background, an approach to Teichmüller theory of compact oriented Riemann surfaces is outlined which then is extended to oriented R

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Euler Characteristic and Morse Theory for?Minimal Surfacesroperties. The most interesting case .=3 is much more difficult than the case .≥4 since, according to the index theorem, for .=3 the nondegenerate minimal surfaces are not generic. Nevertheless it will be useful to have a theory for .≥4 as one can connect ?.-contours via homotopies in ?. with ?.-con

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