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arXiv · 0909.1963

Finite type annular ends for harmonic functions

William H. Meeks III·Joaquin Perez
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Abstract

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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William H. Meeks III, Joaquin Perez. 2009-09-10. Finite type annular ends for harmonic functions. https://arxiv.org/abs/0909.1963

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