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.
The L2-Structure of Moduli spaces of Einstein Metrics on 4-Manifolds.
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...
The manifold of Euclidean inner products of sphere.
The Moduli Space of Complete Embedded Constant Mean Cuvature Surfaces.
The moduli space of special lagrangian submanifolds