2004/08/05 by Brian Dean, Brian C. Dean, Dean, Brian
Mathematics · #57R40 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 53C42 #Secondary 53A10 #math.DG #msc:53A10 #msc:53C42 #msc:57R40
paper · pdf · doi:10.48550/arxiv.math/0408079
10 pages, 0 figures, preprint
arxiv created 2004/08/05 · openalex publication_date 2004/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a prescribed discrete (and hence, finite) set of points on the x3-axis. This extends a result of Colding and Minicozzi, who constructed a sequence for which the curvature blows up only at the center of the ball, and is a partial affirmative answer to the larger question of the existence of a sequence for which the curvature blows up precisely on a prescribed closed set on the x3-axis.