On the asymptotic behaviour of a solution of a differential equation in a Hilbert space
On the Convenient Setting for Real Analytic Mappings.
On the creation of conjugate points.
On the differential geometry of some classes of infinite dimensional manifolds
Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space of any manifold . The name comes from the fact that various elements of the geometry of are constructed via lifting of the corresponding elements of the geometry of . In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to . In order to define a lifted...
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the first homology of automorphism groups of manifolds with geometric structures
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.
On the fundamental group of the space of harmonic 2-spheres in the n-sphere.
On the geometry of free loop spaces.
On the geometry of the Virasoro-Bott group.
On the group of real analytic diffeomorphisms
The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.
On the homeomorphism groups of manifolds and their universal coverings
Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.
On the Homotopy Type of Certain Spaces of Differentiable Maps.
On the homotopy type of and connected problems
This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms of a differentiable compact manifold (with -topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo (with -topology). As a biproduct, one gets new facts about the homotopy groups of , and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section...
On the relation between the Einstein and the Komar expressions for the energy of the gravitational field
On the space of asymptotically euclidean metrics
On the Space of the Linear Homeomorphisms of a Polyhedral TV-Cell with Two Interior Vertices*.
On the stratification of the orbit space for the action of automorphisms on connections [Book]
On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
On the theory of Sobolev-type classes of functions with values in a metric space.
On the uniform perfectness of groups of bundle homeomorphisms
Groups of homeomorphisms related to locally trivial bundles are studied. It is shown that these groups are perfect. Moreover if the homeomorphism isotopy group of the base is bounded then the bundle homeomorphism group of the total space is uniformly perfect.