Karen K. Uhlenbeck

Publications91
h-index34
Citations7,299
Highly Influential Citations666
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The Existence of Minimal Immersions of 2-Spheres
Connections withLP bounds on curvature
We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inRn when the integralLn/2 field norm is sufficiently small. We then are able to prove a weak…
On the existence of hermitian‐yang‐mills connections in stable vector bundles
A regularity theory for harmonic maps
0. Introduction In this paper we develop a regularity theory for energy minimizing harmonic maps into Riemannian manifolds. Let u: M -> N be a map between Riemannian manifolds of dimension n and k.…
Instantons and Four-Manifolds
This volume has been designed to explore the confluence of techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional…
Harmonic maps into Lie groups: classical solutions of the chiral model
On considere deux aspects de la structure algebrique de #7B-M, l'espace des applications harmoniques d'un domaine a 2 dimensions simplement connexe dans un groupe de Lie reel G R , la forme reelle…
Boundary regularity and the Dirichlet problem for harmonic maps
In a previous paper [10] we developed an interior regularity theory for energy minimizing harmonic maps into Riemannian manifolds. In the first two sections of this paper we prove boundary regularity…
Regularity for a class of non-linear elliptic systems
where ~ is a smooth positive function satisfying the ellipticity condition o(Q) + 2~'(Q)q > 0, V denotes the gradient, and [Vs[2 = ~ = 1 ]Vskl 2. This type of system arises as the EulerLagrange…
Generic Properties of Eigenfunctions
Removable singularities in Yang-Mills fields
We show that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite. We obtain the result that every…
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