Symmetric log-epiperimetric inequality for harmonic maps with analytic target and applications

TL;DR

This paper introduces a symmetric log-epiperimetric inequality for harmonic maps with analytic targets, providing new proofs of tangent uniqueness and insights into the asymptotic behavior of energy minimizing harmonic maps.

Contribution

It establishes a novel symmetric (log)-epiperimetric inequality and applies it to prove tangent uniqueness and analyze asymptotic properties of harmonic maps.

Findings

New proof of tangent uniqueness for harmonic maps with isolated singularities.

Uniqueness of tangents at infinity for harmonic maps with controlled energy growth.

Development of a symmetric (log)-epiperimetric inequality for harmonic maps.

Abstract

We establish a direct symmetric (log)-epiperimetric inequality for harmonic maps with analytic target and we leverage on this result to achieve a new proof of Simon's celebrated uniqueness of tangents with isolated singularity for energy minimizing harmonic maps. Moreover, we show that tangents at infinity of energy minimizing harmonic maps with suitably controlled energy growth are always unique, by exploiting the lower bound entailed in the symmetric (log)-epiperimetric inequality.