3 papers
math.DG2005
A generalization of Rado's Theorem for almost graphical boundaries
Brian Dean, Giuseppe Tinaglia
In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical bou…
math.DG2004
Embedded minimal disks with prescribed curvature blowup
Brian Dean
We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at…
math.DG2003
Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds
Brian Dean
Let M be a 3-manifold (possibly with boundary). We show that, for any positive integer g, there exists an open nonempty set of metrics on M for each of which there are stable compa…