Elliptic partial differential equations and ordinary differential equations in Banach space
Summary: We prove a characterization of the immersions in the context of infinite dimensional manifolds with corners, we prove that a Hausdorff paracompact -manifold whose charts are modelled over real Banach spaces which fulfil the Urysohn -condition can be embedded in a real Banach space, , by means of a closed embedding, , such that, locally, its image is a totally neat submanifold of a quadrant of a closed vector subspace of and finally we prove that a Hausdorff paracompact topological...
The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps he thinks of the meson fields as of global sections in a bundle . For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with , one has where is the universal bundle...
This paper contains the lectures given by the author at the Winter School on “Geometry and Physics” in Srní 2001. These lectures are based on two recent works of the author with A. Korányi and on a forthcoming paper with K. Johnson and A. Korányi. In the paper results are presented concerning equivariant differential operators on homogeneous spaces (section 1), first order equivariant differential operators on boundaries of symmetric spaces (section 2), the Poisson transform (section 3) and complex...