Brownian motion and the parabolicity of minimal graphs

Details Brownian motion and the parabolicity of minimal graphs Brownian motion and the parabolicity of minimal graphs

2008-10-03

arxiv.org/abs/0810.0669v1

Mathematics

Differential Geometry

7 pages

Scientific paper

We prove that minimal graphs (other than planes) are parabolic in the sense
that any bounded harmonic function is determined by its boundary values. The
proof relies on using the coupling introduced in the author's earlier paper "A
martingale approach to minimal surfaces" to show that Brownian motion on such a
minimal graph almost surely strikes the boundary in finite time.

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