Embedded minimal disks: Proper versus nonproper—global versus local-Reference-Cited by-同舟云学术

Embedded minimal disks: Proper versus nonproper—global versus local

Published:2003-08-25 Issue:1 Volume:356 Page:283-289
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Colding Tobias,Minicozzi William

Abstract

We construct a sequence of compact embedded minimal disks in a ball in R 3 \mathbf {R}^3 with boundaries in the boundary of the ball and where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper. If instead the sequence of embedded disks had boundaries in a sequence of balls with radii tending to infinity, then we have shown previously that any limit must be smooth and proper.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2004-356-01/S0002-9947-03-03230-6/S0002-9947-03-03230-6.pdf

Reference3 articles.

1. [CM1] T.H. Colding and W.P. Minicozzi II, Embedded minimal disks, To appear in The Proceedings of the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces. MSRI. math.DG/0206146.

2. [CM2] \bysame, The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected, preprint, math.AP/0210119.

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