On the geometry of the Virasoro-Bott group.
On the global stable manifold
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general Banach setting gives rise to subtle questions about the possibility of extending germs of diffeomorphisms.
On the homotopical classification of DJ-mappings of infnitely dimensional spheres
On the Kähler geometry of the Hilbert-Schmidt Grassmannian.
On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the quantum groups and semigroups of maps between noncommutative spaces
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are...
On the radical of J*-triples.
On the size of the sets of gradients of bump functions and starlike bodies on the Hilbert space
We study the size of the sets of gradients of bump functions on the Hilbert space , and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in can be. We find that those sets can be quite small. On the one hand, the usual norm of the Hilbert space can be uniformly approximated by smooth Lipschitz functions so that the cones generated by the ranges of its derivatives have empty interior. This implies that there are smooth Lipschitz bumps...
On the structure of Hilbert cube manifolds
On the Structure of Manifolds with positive Scalar Curvature.
On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
On the transverse Scalar Curvature of a Compact Sasaki Manifold
We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson [10, 11], which involves the geometry of infinitedimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modification. We prove that the space of Sasaki metrics is an infinite dimensional symmetric space and that the transverse scalar curvature of a Sasaki metric is a moment map of the...
On the -equation in a Banach space
Operator inequalities, geodesics and interpolation
Ordinary differential equations on infinite dimensional manifolds.