The CalabiYau conjectures for embedded surfaces
Tobias H. Colding, William P. Minicozzi II,
2004.04.09
http://arxiv.org/abs/math/0404197
In this paper we will prove the CalabiYau conjectures for embedded surfaces.
In fact, we will prove considerably more.
The CalabiYau conjectures about surfaces date back to the 1960s. Much work
has been done on them over the past four decades. In particular, examples of
JorgeXavier 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.
