3 papers
math.DG2024
Differential Operators on Non-compact Harmonic Manifolds
Oliver Brammen
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution a…
math.DG2023
The Brownian Motion on Harmonic Manifolds of Purely Exponential Volume Growth
Oliver Brammen
We show that Sullivan's method of constructing eigenfunctions of the Laplacian \cite{Sullivan1987RelatedAO} is applicable to non-compact simply connected harmonic manifolds of pure…
math.DG2023
Dynamics of -Multiplier for on Harmonic Manifolds of Purely Exponential Volume Growth
Oliver Brammen
We study the dynamics of -multipliers on non-compact simply connected harmonic manifolds of purely exponential volume growth. These are linear operators on the -spaces wh…