Embedding of open riemannian manifolds by harmonic functions

Isometric Embedding of Riemannian Manifolds

Discretization of bounded harmonic functions on Riemannian manifolds and entropy

We give conditions under which the space of bounded harmonic functions on a Riemannian manifold M is naturally isomorphic to the space of bounded harmonic functions of a Markov chain on a discrete net X M arising from a discretization procedure for the pair (M; X). If, further, M is a regular covering manifold and the net is invariant with respect to the deck transformation group, then the entr...

LOCAL GRADIENT ESTIMATE FOR p-HARMONIC FUNCTIONS ON RIEMANNIAN MANIFOLDS

For positive p-harmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension n, p and the radius of the ball on which the function is de…ned. Our approach is based on a careful application of the Moser iteration technique and is di¤erent from Cheng-Yau’s method [2] employed ...

Harmonic Morphisms between Riemannian Manifolds

Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...

Harmonic Quasiconformal Mappings of Riemannian Manifolds