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Dec 8, 2008 3:00 pm (Monday)
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Event details: Robert Neel Minimal surfaces and coupled Brownian motion.
Description
Abstract: We introduce an extrinsic analogue, for minimal surfaces in R3, of the mirror coupling of two Brownian motions and use it to prove geometric results. The first class of results we look at are strong halfspace-type theorems, in which the goal is to prove that pairs of minimal surfaces, under some conditions, must intersect. Second, we study harmonic functions on minimal surfaces, proving that properly embedded minimal surfaces of bounded curvature admit no non-constant bounded harmonic functions (thus making progress toward a conjecture of Sullivan) and that non-planar minimal graphs are parabolic (thus proving a conjecture of Meeks).
Location Information:
Homewood - Krieger
Room: 304
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