PACIFIC JOURNAL OF MATHEMATICS 256(2) 317-357 2012年4月 [査読有り]
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in R-n, and investigate its properties. Two guiding principles are given by Milnor's way of measuring using a local Crofton-type formula, and by cons...
JOURNAL OF GEOMETRIC ANALYSIS 21(3) 743-766 2011年7月 [査読有り]
We continue the study of minimal singular surfaces obtained by a minimization of a weighted energy functional in the spirit of J. Douglas's approach to the Plateau problem. Modeling soap films spanning wire frames, a singular surface is the union ...