Harmonic Functions on Rank One Asymptotically Harmonic Manifolds

Harmonic Functions on Classical Rank One Balls

On 3-dimensional Asymptotically Harmonic Manifolds

Let (M, g) be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show thatM is a hyperbolic manifold of constant sectional curvature −h 2 4 , provided M is asymptotically harmonic of constant h > 0.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Finite rank harmonic operator-valued functions

The purpose of this paper is to characterize when a harmonic function with values in the finite rank operators on a Hilbert space is expressible as a harmonic matrix-valued function. We show that harmonic function with values in the rank 1 normal operators is expressible as a harmonic matrix-valued function. We also prove that for any natural number, n, a harmonic function with values in the ra...

stable exponentially harmonic maps between finsler manifolds