On parabolicity and area growth of minimal surfaces

Details On parabolicity and area growth of minimal surfaces On parabolicity and area growth of minimal surfaces

2010-04-26

arxiv.org/abs/1004.4544v2

Mathematics

Differential Geometry

14 pages, sections 3 and 4 generalized, reference added, typos corrected

Scientific paper

We establish parabolicity and quadratic area growth for minimal surfaces-with-boundary contained in regions of R^3 which are within a sub-logarithmic factor of the exterior of a cone. Unlike previous work showing that these two properties hold for minimal surfaces-with-boundary contained between two catenoids, we do not make use of universal superharmonic functions. Instead, we use stochastic methods, which have the additional feature of giving a type of parabolicity in a more general context than Brownian motion on a minimal surface.

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