Chern-Osserman type equality for complete surfaces in R^n
Differential Geometry
2018-04-18 v1
Abstract
We obtain a Chern-Osserman type equality of a complete properly immersed surface in Euclidean space, provided the L^2-norm of the second fundamental form is finite. Also, by using a monotonicity formula, we prove that if the L^2-norm of mean curvature of a noncompact surface is finite, then it has at least quadratic area growth.
Cite
@article{arxiv.1703.07543,
title = {Chern-Osserman type equality for complete surfaces in R^n},
author = {Qing Chen and Wenjie Yang},
journal= {arXiv preprint arXiv:1703.07543},
year = {2018}
}