2010 **Abstract:** With contributions by (2010): 49Q05, 53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20, 30C20 c Springer-Verlag Berlin Heidelberg 1992, 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the…

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“…Boundary regularity results were obtained in a variety of settings. Interested readers are encouraged to consult the recent treatise [8] [9] on boundary value problems of minimal surfaces.…”

confidence: 99%

“…Then we immerse this configuration < Γ, Z > into a soap liquid, and a soap pellicle is installed which minimizes the area and is bounded by the thin wire Γ. Moreover, this minimal surface possesses a trace on the cylinder In particular for the well-established theory of minimal graphs with mixed boundary conditions of Dirichlet and Neumann, we refer our readers to the book [1] by U. Dierkes, S. Hildebrandt, and F. Sauvigny as well as to the following books by U. Dierkes, S. Hildebrandt, and A. Tromba [2] and [3] on the theory of minimal surfaces, which appeared within the Springer-Grundlehren in September 2010. In the geometric situation of our winding staircase, a minimal graph over a Riemannian surface R appears.…”

confidence: 99%

“…In [2], Dierkes, Hildebrandt and Tromba introduced the method of taking higher-order derivatives of Dirichlet's energy in the direction of forced Jacobi fields, discovered by both Böhme and Tromba, to treat the question of interior branch points. The calculation of higher-order derivatives was achieved by applying the theory of residues.…”

confidence: 99%

“…The cases 1 + m = 2(n + 1) and 1 + m = 3(n + 1) are called exceptional. The notion of exceptional is the infinitesimal notion of analytically false [2].…”

mentioning

confidence: 99%