Polysuperharmonic functions on a harmonic space

Some Harmonic Functions on Minkowski Space

This note presents elementary geometric descriptions of several simple families of harmonic functions on the upper sheet of the unit hyperboloid in Minkowski three-space. As is briefly discussed here, these calculations grew out of an earlier attempt to construct Poincaré series on punctured surfaces using Minkowski geometry. Introduction The material in this note grew out of an attempt (discus...

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

Harmonic Functions, Entropy, and a Characterization of the Hyperbolic Space

Let (Mn; g) be a compact Riemannian manifold with Ric (n 1). It is well known that the bottom of spectrum 0 of its unverversal covering satis…es 0 (n 1) =4. We prove that equality holds i¤ M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. 1. Introduction Complete Riemannian manifolds with nonnegative Ricci curvature have been intensively studied by many people and...

More on Harmonic Functions

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.