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arXiv · 1407.0679

A Fatou theorem for $F$-harmonic functions

Sébastien Alvarez
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Abstract

In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call $F$-harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral representation analogous to the Poisson representation of harmonic functions, where the role of the Poisson kernel is played by a H\"older continuous kernel. More precisely we prove a theorem \`a la Fatou about the nontangential convergence of quotients of such functions, from which we deduce some basic properties such as the uniqueness of the $F$-harmonic function on a compact manifold and of the integral representation of $F$-harmonic functions.

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Sébastien Alvarez. 2014-07-02. A Fatou theorem for $F$-harmonic functions. https://arxiv.org/abs/1407.0679

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