A LIP Immersion of Lipschitz Manifolds Modelled on Some Banach Spaces
Banach-Stone Theorems for Banach Manifolds.
H1/2 maps with values into the circle : minimal connections, lifting, and the Ginzburg–Landau equation
Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.
We show how an operation of inf-convolution can be used to approximate convex functions with C1 smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.
Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits
In this paper, we construct a hyperkähler structure on the complexification of any Hermitian symmetric affine coadjoint orbit of a semi-simple -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of . By a relevant identification of the complex orbit with the cotangent space of induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on compatible with...
On Lipschitz and d.c. surfaces of finite codimension in a Banach space
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated -ideals are studied. These -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.
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...
Open Subsets of LF-spaces
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.