18 citations · 63 across the 18 of their papers we have counts for
7 papers · 1 filter
A Note on Moving Frames along Sobolev Maps and the Regularity of Weakly Harmonic Maps
Luigi Appolloni, Ben Sharp
The purpose of this note is twofold. First we show that, for weakly differentiable maps between Riemannian manifolds of any dimension, a smallness condition on a Morrey-norm of the…
Low-energy -harmonic maps into the round sphere
Ben Sharp
We classify low-energy -harmonic maps from a closed non-spherical Riemannian surface of constant curvature to the round sphere via their bubble scales and centres. In partic…
Łojasiewicz inequalities near simple bubble trees
Andrea Malchiodi, Melanie Rupflin, Ben Sharp
In this paper we prove a gap phenomenon for critical points of the -functional on closed non-spherical surfaces when is constant, and in this setting furthermore prove that…
Global estimates and energy identities for elliptic systems with antisymmetric potentials
Tobias Lamm, Ben Sharp
We derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensi…
Critical problems in one complex dimension and some remarks on conformally invariant variational problems in two real dimensions
Ben Sharp
We will study a linear first order system, a connection $\db$ problem, on a vector bundle equipped with a connection, over a Riemann surface. We show optimal conditions on the conn…
Higher integrability for solutions to a system of critical elliptic PDE
Ben Sharp
We give new estimates for a critical elliptic system introduced by Rivière-Struwe in \cite{riviere_struwe} (see also the work of Rupflin \cite{rupflin} and Schikorra \cite{schikorr…