The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.
The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
The -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
The behaviour of the Gaussian beam in an anisotropic medium with an interface between two media.
The Bellaterra connection.
A new object is introduced - the "Fischer bundle". It is, formally speaking, an Hermitean bundle of infinite rank over a bounded symmetric domain whose fibers are Hilbert spaces whose elements can be realized as entire analytic functions square integrable with respect to a Gaussian measure ("Fischer spaces"). The definition was inspired by our previous work on the "Fock bundle". An even more general framework is indicated, which allows one to look upon the two concepts from a unified point of view....
The BIC of a singular foliation defined by an abelian group of isometries
We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group G is compact...
The Blow-Up of p-Harmonic maps.
The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.
The bottom of the spectrum of a Riemannian covering.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of the boundaries.
The bounds for the squared norm of the second fundamental form of minimal submanifolds of .
The brachistochrone problem with frictional forces
The brachistochrone problem with frictional forces
In this paper we show the existence of the solution for the classical brachistochrone problem under the action of a conservative field in presence of frictional forces. Assuming that the frictional forces and the potential grow at most linearly, we prove the existence of a minimizer on the travel time between any two given points, whenever the initial velocity is great enough. We also prove the uniqueness of the minimizer whenever the given points are sufficiently close.
The hypothesis in Pesin theory
The Calabi functional on a ruled surface
We study the Calabi functional on a ruled surface over a genus two curve. For polarizations which do not admit an extremal metric we describe the behavior of a minimizing sequence splitting the manifold into pieces. We also show that the Calabi flow starting from a metric with suitable symmetry gives such a minimizing sequence.
The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories
As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical...
The Canonical Class and the Properties of Kähler Surfaces.
The canonical constructions of connections on total spaces of fibred manifolds
We classify classical linear connections on the total space of a fibred manifold induced in a natural way by the following three objects: a general connection in , a classical linear connection on and a linear connection in the vertical bundle . The main result says that if and then the natural operators under consideration form the dimensional affine space.