A short note on the mean exit time of the Brownian motion

CADEDDU, LUCIO;FARINA, MARIA ANTONIETTA

2017-01-01

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Abstract

We investigate the functional (Formula presented.) where (Formula presented.) runs through the set of compact domains of fixed volume (Formula presented.) in any Riemannian manifold (Formula presented.) and where (Formula presented.) is the mean exit time from (Formula presented.) of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of (Formula presented.) are harmonic domains.