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.

scholarly journals Should We Solve Plateau’s Problem Again?

2014 ◽  
Author(s):  
Guy David
Keyword(s):  
Local Regularity ◽  
Plateau Problem ◽  
Soap Films ◽  
Plateau’S Problem ◽  
Minimization Problems ◽  
Minimal Sets ◽  
Modeling Problem ◽  
Regularity Properties ◽  
Plateau's Problem ◽  
Regularity Results

This chapter gives a partial account of the situation of Plateau's problem on the existence and regularity of soap films with a given boundary. It starts with a description of some of the most celebrated solutions of Plateau's problem, followed by a description of a few easy examples. The chapter then returns to the modeling problem and mentions a few additional ways to state a Plateau problem. It briefly describes the known local regularity properties of the Almgren minimal sets, and why we would like to extend some of these regularity results to sliding minimal sets, all the way to the boundary. At the same time, the chapter considers why these solutions are not always entirely satisfactory. Finally, the chapter explains why the regularity results for sliding Almgren minimal sets also apply to solutions of the Reifenberg and size minimization problems described earlier in the chapter.

Numerical simulation of Plateau’s problem of minimal surfaces using nonvariational finite element method

2016 ◽  
Vol 33 (5) ◽  
pp. 1490-1507 ◽  
Author(s):  
Garima Mishra ◽  
Manoj Kumar
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Minimal Surfaces ◽  
Design Methodology ◽  
Engineering Application ◽  
Content Type ◽  
Plateau’S Problem ◽  
Plateau's Problem ◽  
Element Method

Purpose – Numerical solution of Plateau’s problem of minimal surface using non-variational finite element method. The paper aims to discuss this issue. Design/methodology/approach – An efficient algorithm is proposed for the computation of minimal surfaces and numerical results are presented. Findings – The solutions obtained here are examined for different cases of non-linearity and are found sufficiently accurate. Originality/value – The manuscript provide the non-variational solution for Plateau’s problem. Thus it has a good value in engineering application.

scholarly journals Existence Results for the Conformal Dirac–Einstein System

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chiara Guidi ◽  
Ali Maalaoui ◽  
Vittorio Martino
Keyword(s):  
Perturbation Methods ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Existence Results ◽  
First Variation ◽  
The First Variation

AbstractWe consider the coupled system given by the first variation of the conformal Dirac–Einstein functional. We will show existence of solutions by means of perturbation methods.

Description of a 3-periodic minimal surface family with trigonal symmetry

1994 ◽  
Vol 209 (1) ◽  
Author(s):  
A. Fogden
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Systematic Analysis ◽  
Trigonal Symmetry ◽  
Triply Periodic Minimal Surfaces ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
The Family

AbstractA systematic analysis of a family of triply periodic minimal surfaces of genus seven and trigonal symmetry is given. The family is found to contain five such surfaces free from self-intersections, three of which are previously unknown. Exact parametrisations of all surfaces are provided using the Weierstrass representation.

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