Robert Gulliver ( University of Minnesota )
Title:	Curvature of boundaries and density estimates of minimal submanifolds
Abstract:	Eckholm, White and Wienholtz showed that a minimal surface in R^n spanning a curve of total curvature less than 2k\pi has density less than the integer k. Of particular interest is the embedding result k=2. I will indicate how this density result is extended (1) to an ambient manifold with an upper bound on sectional curvatures, and (2) to a boundary which is a topological graph, with a specific notion of total curvature. We have partial results for higher-dimensional minimal submanifolds. This includes joint work with Jaigyoung Choe and Sumio Yamada.