scholarly journals The affine Plateau problem

2005 ◽  
Vol 18 (2) ◽  
pp. 253-289 ◽  
Author(s):  
Neil S. Trudinger ◽  
Xu-Jia Wang
Keyword(s):  
Plateau Problem

scholarly journals On the Levi-flat Plateau problem

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Jiří Lebl ◽  
Alan Noell ◽  
Sivaguru Ravisankar
Keyword(s):  
Plateau Problem ◽  
Flat Plateau

scholarly journals Kohn-Rossi cohomology and its application to the complex plateau problem, II

2007 ◽  
Vol 77 (1) ◽  
pp. 135-148 ◽  
Author(s):  
Hing Sun Luk ◽  
Stephen S.-T. Yau
Keyword(s):  
Plateau Problem

scholarly journals On solving the plateau problem in parametric form

1983 ◽  
Vol 6 (2) ◽  
pp. 341-361
Author(s):  
Baruch cahlon ◽  
Alan D. Solomon ◽  
Louis J. Nachman
Keyword(s):  
Minimal Surface ◽  
Numerical Method ◽  
Minimal Surfaces ◽  
Plateau Problem ◽  
Parametric Form ◽  
First Variation ◽  
Plateau’S Problem ◽  
Numerical Example ◽  
Plateau's Problem ◽  
The First Variation

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.

Das Plateau-Problem

2014 ◽  
pp. 133-170
Author(s):  
Jost-Hinrich Eschenburg ◽  
Jürgen Jost
Keyword(s):  
Plateau Problem

scholarly journals Maximal metric surfaces and the Sobolev-to-Lipschitz property

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Paul Creutz ◽  
Elefterios Soultanis
Keyword(s):  
Metric Spaces ◽  
Equivalence Classes ◽  
Plateau Problem ◽  
Lipschitz Property ◽  
Maximality Condition ◽  
Volume Rigidity

Abstract We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak–Wenger, which satisfies a related maximality condition.

Sign in / Sign up

Export Citation Format

Share Document