We construct a local action of the group of rational maps from S to GL(n, C) on local solutions of flows of the ZS-AKNS sl(n, C)-hierarchy. We show that the actions of simple elements (linear… (More)

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… (More)

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… (More)

Complete, conformally flat metrics of constant positive scalar curvature on the complement of k points in the n-sphere, k ≥ 2, n ≥ 3, were constructed by R. Schoen in 1988. We consider the problem of… (More)

Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a… (More)

The Yang-Mills functional for connections on principle SU(2) bundles over S(4) is studied. Critical points of the functional satisfy a system of second-order partial differential equations, the… (More)

Survey article based on lectures given by the first author in May 2001 during 4th SIGRAV and SAGP2001 Graduate School. The focus of these lectures is the Gopakumar-Vafa's insight that " Large N… (More)

We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for… (More)

We construct a gauge theoretic change of variables for the wave map from R × R into a compact group or Riemannian symmetric space, prove a new multiplication theorem for mixed Lebesgue-Besov spaces,… (More)

parameterized by θ ∈ R. But we do not expect that the “sum” of two such solutions will again be a solution. However, the special class of soliton equations, the subject of this article, does have a… (More)