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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 30
  3. Calculus of Variations and Partial Differential Equations : Volume 30, Issue 4, December 2007
  4. Schwarz operators of minimal surfaces spanning polygonal boundary curves
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 30, Issue 4, December 2007
Large solutions for biharmonic maps in four dimensions
Some homogenization results for non-coercive Hamilton–Jacobi equations
Schwarz operators of minimal surfaces spanning polygonal boundary curves
Minimal energy configurations of strained multi-layers
Geometric evolution equations in critical dimensions
The Dirichlet problem for constant mean curvature surfaces in Heisenberg space
Existence and regularity for generalised harmonic maps associated to a nonlocal polyconvex energy of Skyrme type
A simple proof of removable singularities for coupled fermion fields
Calculus of Variations and Partial Differential Equations : Volume 30, Issue 3, November 2007
Calculus of Variations and Partial Differential Equations : Volume 30, Issue 2, October 2007
Calculus of Variations and Partial Differential Equations : Volume 30, Issue 1, September 2007
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Schwarz operators of minimal surfaces spanning polygonal boundary curves

Content Provider SpringerLink
Author Jakob, Ruben
Copyright Year 2007
Abstract This paper examines the Schwarz operator A and its relatives Ȧ, Ā and Ǡ that are assigned to a minimal surface X which maps consequtive arcs of the boundary of its parameter domain onto the straight lines which are determined by pairs P j , P j+1 of two adjacent vertices of some simple closed polygon $${\Gamma\subset \mathbb{R}^3}$$ . In this case X possesses singularities in those boundary points which are mapped onto the vertices of the polygon Γ. Nevertheless it is shown that A and its closure Ā have essentially the same properties as the Schwarz operator assigned to a minimal surface which spans a smooth boundary contour. This result is used by the author to prove in [Jakob, Finiteness of the set of solutions of Plateau’s problem for polygonal boundary curves. I.H.P. Analyse Non-lineaire (in press)] the finiteness of the number of immersed stable minimal surfaces which span an extreme simple closed polygon Γ, and in [Jakob, Local boundedness of the set of solutions of Plateau’s problem for polygonal boundary curves (in press)] even the local boundedness of this number under sufficiently small perturbations of Γ.
Ending Page 476
Page Count 10
Starting Page 467
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 4
Volume Number 30
Language English
Publisher Springer-Verlag
Publisher Date 2007-02-22
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Estimation of eigenvalues, upper and lower bounds Minimal surfaces Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical and Computational Physics Analysis Applications to minimal surfaces (problems in two independent variables)
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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