Estimates for the energy density of critical points of a class of conformally invariant variational problems

TL;DR

This paper demonstrates that the energy density of critical points in certain conformally invariant variational problems with small energy is in the local Hardy space h^1, leading to new proofs of energy convexity and uniqueness for weakly harmonic maps.

Contribution

It establishes the Hardy space regularity of energy density for critical points, providing novel proofs for energy convexity and uniqueness in harmonic map theory.

Findings

Energy density lies in local Hardy space h^1 for small energy.

Provides a new proof of energy convexity for weakly harmonic maps.

Shows uniqueness of weakly harmonic maps with small energy.

Abstract

We show that the energy density of critical points of a class of conformally invariant variational problems with small energy on the unit 2-disk B_1 lies in the local Hardy space h^1(B_1). As a corollary we obtain a new proof of the energy convexity and uniqueness result for weakly harmonic maps with small energy on B_1.