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Complete surfaces of at most quadratic area growth. (English) Zbl 1008.53034
Summary: 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.

MSC:
53C20 Global Riemannian geometry, including pinching
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