arXiv 0810.06692008-10-03math.DGmath.PR

Brownian motion and the parabolicity of minimal graphs

Robert W. Neel

备注：: 7 pages

英文摘要：

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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