Extending Infinity Harmonic Functions by Rotation

Extending Functions in the Model Subspaces of H^2(R) to C

An Introduction of Infinity Harmonic Functions

This note serves as a basic introduction on the analysis of infinity harmonic functions, a subject that has received considerable interests very recently. The author discusses its connection with absolute minimal Lipschitz extension, present several equivalent characterizations of infinity harmonic functions. He presents the celebrated theorem by R. Jensen [17] on the uniqueness of infinity har...

Weak Fubini Property and Infinity Harmonic Functions in Riemannian and Sub-riemannian Manifolds

We examine the relationship between infinity harmonic functions, absolutely minimizing Lipschitz extensions, strong absolutely minimizing Lipschitz extensions, and absolutely gradient minimizing extensions in CarnotCarathéodory spaces. Using the weak Fubini property we show that absolutely minimizing Lipschitz extensions are infinity harmonic in any sub-Riemannian manifold.

Classifications of some special infinity-harmonic maps

∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞-harmonic maps from and into a sphere, quadratic ∞-harmonic maps between Euclidean spaces. We describe all linear and quadratic ∞-harmonic maps between Nil and Euclidean spaces, b...

Phragmén–lindelöf Theorem for Infinity Harmonic Functions

We investigate a version of the Phragmén–Lindelöf theorem for solutions of the equation ∆∞u = 0 in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the p-harmonic equation when p tends to ∞.