Minimizing functionals depending on surfaces and their curvatures: A class of variational problems in the setting of generalized Gauss graphs
Silvano Delladio · Pacific Journal of Mathematics · 1997
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.and let C (j) h , j = 1, . . ., h, denote the "double-teeth" that form C h ; here there is an explanatory figure, in the case h = 3.