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

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.

17 pages

Cited by in corpus (8)

• Min-max minimal disks with free boundary in Riemannian manifolds
• Uniformity of harmonic map heat flow at infinite time
• Non-existence of a Wente's $L^{\infty }$ estimate for the Neumann problem
• Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold
• Uniqueness of Dirac-harmonic maps from a compact surface with boundary
• Global estimates and energy identities for elliptic systems with antisymmetric potentials
• Critical $\bar{\partial }$ problems in one complex dimension and some remarks on conformally invariant variational problems in two real dimensions
• Uniqueness of conformal-harmonic maps on locally conformally flat 4-manifolds