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arXiv · 2311.02977

The Brownian Motion on Harmonic Manifolds of Purely Exponential Volume Growth

Oliver Brammen
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Abstract

We show that Sullivan's method of constructing eigenfunctions of the Laplacian \cite{Sullivan1987RelatedAO} is applicable to non-compact simply connected harmonic manifolds of purely exponential volume growth. Thereby we extend the case of pinched negative curvature to non-symmetric Damek-Ricci spaces.

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Oliver Brammen. 2023-11-06. The Brownian Motion on Harmonic Manifolds of Purely Exponential Volume Growth. https://arxiv.org/abs/2311.02977

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