Minimizing functionals depending on surfaces and their curvatures: A class of variational problems in the setting of generalized Gauss graphs

Silvano Delladio

Vol. 179 (1997), No. 2, 301–323

DOI: 10.2140/pjm.1997.179.301

Abstract

We consider a family of variational problems involving generalized Gauss graphs. Roughly, we are interested in the problem of minimizing a functional defined in a class of surfaces constrained to include a given fixed rectifiable set. As a particular case, one has the following example: Given a rectifiable set M, find a mass minimizer among all null boundary generalized Gauss graphs of surfaces which include M as a subset. Particular attention is paid to the case of curves in the plane.

Milestones

Received: 21 December 1995

Published: 1 June 1997