In this article, we study complete surfaces with finite topological type and has at most quadratic area growth. In particular, we show that if the curvature of such a surface does not change sign, then it must be of finite total curvature.
Cite this article
P. Li, Complete surfaces of at most quadratic area growth. Comment. Math. Helv. 72 (1997), no. 1, pp. 67–71DOI 10.1007/PL00000367