Of the structure of the Euler mapping
On a class of weighted function spaces and related pseudodifferential operators
On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.
On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces
On representation of functionals of local type by differential forms
On some questions of topology for S1-valued fractional Sobolev spaces.
On symmetrically growing bodies.
This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.
On the Convenient Setting for Real Analytic Mappings.
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 fundamental group of the space of harmonic 2-spheres in the n-sphere.
On the geometry of free loop spaces.
On the theory of Sobolev-type classes of functions with values in a metric space.
Recent developments in the theory of function spaces
Representation of a gauge group as motions of a Hilbert space
This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second...
Representations of the group of functions taking values in a compact Lie group
Riemannian geometries on spaces of plane curves
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Smooth structures on
Spaces of approximate fibrations on Hilbert cube manifolds
Spaces of measurable functions
For a metrizable space X and a finite measure space (Ω, , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.
Spaces of polynomials with roots of bounded multiplicity
We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.