On Plateau's Problem for Soap Films with a Bound on Energy
Abstract
We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, integral currents, nonorientable surfaces and soap films as observed by Plateau with a bound on energy. Our area minimizing solution is shown to be a smooth surface away from its branched set which is a union of Lipschitz Jordan curves of finite total length.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403333
 Bibcode:
 2004math......3333H
 Keywords:

 Differential Geometry;
 Mathematical Physics;
 28A75;
 49Q15
 EPrint:
 13 pages, 1 figure