The abstract Riemannian path space.
The Approximation of Instantons.
The Atiyah-Jones conjecture for ruled surfaces.
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
The closure of the space of homeomorphisms on a manifold. The piecewise linear case
The cohomology of holomorphic self maps of the Riemann sphere.
The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces.
The deformation theory of anti-self-dual conformal structures.
The diameter of the symplectomorphism group is infinite.
The diffeomorphism group of a Lie foliation
We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus , . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for , P. Iglesias and...
The diffeomorphism group of a non-compact orbifold [Book]
The Differentiable Structure of Three Remarkable Diffeomorphism Groups.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The Feynman path integral as an improper integral over the Sobolev space
The geometry of the moduli space of CP2 instantons.
The homology of some groups of diffeomorphisms.
The homotopy type of the space of degree 0 immersed plane curves.
The space Bi0 = Imm0 (S1, R2) / Diff (S1) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups π1(Bi0) = Z, π2(Bi0) = Z, and πk(Bi0) = 0 for k ≥ 3.
The H-theorem for Boltzmann type equations.
The Indes Theorem for k-Fold Connected Minimal Surfaces.
The metric in gauge theory: an introduction and some applications
We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.