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Plateau’s problem for infinite contours
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Friedrich Tomi
Veröffentlicht/Copyright:
25. September 2009
Abstract
Plateau’s problem is solved for a certain class of properly embedded unbounded curves in R3, i.e.the existence of simply connected properly immersed minimal surfaces is shown which have a given curve from this class as their boundary. The class of admissible boundary contours includes all properly embedded piecewise C1,α curves with polynomial ends. The constructed surfaces have quadratic area growth.
Published Online: 2009-09-25
Published in Print: 2009-07
© by Oldenbourg Wissenschaftsverlag, Heidelberg, Germany
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Artikel in diesem Heft
- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
- Boundary regularity via Uhlenbeck–Rivière decomposition
- Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
Artikel in diesem Heft
- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
- Boundary regularity via Uhlenbeck–Rivière decomposition
- Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
