A sufficient condition for a critical point of a functional to be a minimum and its application to Plateau's problem

1983 ◽  
Vol 263 (3) ◽  
pp. 303-312 ◽  
Author(s):  
A. J. Tromba
Keyword(s):  
Critical Point ◽  
Sufficient Condition ◽  
Plateau’S Problem ◽  
Plateau's 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.

Local minimizers of the Willmore functional

Analysis ◽  
2015 ◽  
Vol 35 (2) ◽  
Author(s):  
Florian Skorzinski
Keyword(s):  
Critical Point ◽  
Local Minimizer ◽  
Positive Definite ◽  
Second Derivative ◽  
Sufficient Condition ◽  
Conformal Transformations ◽  
Willmore Functional ◽  
Local Minimizers

AbstractSince the Willmore functional is invariant with respect to conformal transformations and reparametrizations, the kernel of the second derivative of the functional at a critical point will always contain a subspace generated by these transformations. We prove that the second derivative being positive definite outside this space is a sufficient condition for a critical point to be a local minimizer.

Sign in / Sign up

Export Citation Format

Share Document