Finite type annular ends for harmonic functions

Details Finite type annular ends for harmonic functions Finite type annular ends for harmonic functions

2009-09-10

arxiv.org/abs/0909.1963v2

Mathematics

Differential Geometry

11 pages, 3 figures

Scientific paper

In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function. We then apply these results to understand and characterize properly immersed minimal surfaces in $\mathbb{R}^3$ of finite total curvature, in terms of their intersections with two nonparallel planes.

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