Calculus of Variations and Geometric Measure Theory

S. Delladio

Differential geometry on generalized submanifolds

created on 14 Dec 2001


Published Paper

Inserted: 14 dec 2001

Journal: Pacific J. Math.
Volume: 194
Number: 2
Pages: 285-313
Year: 2000


The curvature of a surface can be recovered from the tangent space to the graph of the Gauss map. Exploiting this observation we manage to equip a generalized Gauss graph with the standard tools of differential geometry: Weingarten map, second fundamental form, Riemann curvature tensor. Several variational applications are given.

Keywords: integral currents, generalized curvature, geometric variational problems, generalized Gauss graphs