The Calabi-Yau conjectures for embedded surfaces
Differential Geometry
2007-05-23 v2 Analysis of PDEs
Abstract
In this paper we will prove the Calabi-Yau conjectures for embedded surfaces. In fact, we will prove considerably more. The Calabi-Yau conjectures about surfaces date back to the 1960s. Much work has been done on them over the past four decades. In particular, examples of Jorge-Xavier from 1980 and Nadirashvili from 1996 showed that the immersed versions were false; we will show here that for embedded surfaces, i.e., injective immersions, they are in fact true.
Cite
@article{arxiv.math/0404197,
title = {The Calabi-Yau conjectures for embedded surfaces},
author = {Tobias H. Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:math/0404197},
year = {2007}
}
Comments
To appear in the Annals of Mathematics. Two figures added and introduction expanded