On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian Manifolds

1987 ◽  
pp. 65-75 ◽  
Author(s):  
Jürgen Jost
Keyword(s):  
Riemannian Manifolds ◽  
Minimal Surfaces ◽  
Free Boundaries ◽  
Higher Genus

Minimal Surfaces with Free Boundaries

2010 ◽  
pp. 3-73
Author(s):  
Ulrich Dierkes ◽  
Stefan Hildebrandt ◽  
Anthony J. Tromba
Keyword(s):  
Minimal Surfaces ◽  
Free Boundaries

Approximation of minimal surfaces with free boundaries: convergence results

2018 ◽  
Vol 39 (3) ◽  
pp. 1391-1420
Author(s):  
Tristan Jenschke
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Minimal Surfaces ◽  
Approximate Solutions ◽  
Variational Problems ◽  
Free Boundaries ◽  
Convergence Estimate ◽  
Convergence Results ◽  
Discrete Finite Element

Abstract In a previous paper we developed a penalty method to approximate solutions of the free boundary problem for minimal surfaces by solutions of certain variational problems depending on a parameter $\lambda $. There we showed existence and $C^2$-regularity of these solutions as well as convergence to the solution of the free boundary problem for $\lambda \to \infty $. In this paper we develop a fully discrete finite element procedure for approximating solutions of these variational problems and prove a convergence estimate, which includes an order of convergence with respect to the grid size.

Continuity of minimal surfaces with piecewise smooth free boundaries

1987 ◽  
Vol 276 (4) ◽  
pp. 599-614 ◽  
Author(s):  
J�rgen Jost
Keyword(s):  
Minimal Surfaces ◽  
Piecewise Smooth ◽  
Free Boundaries
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