The algebraic theory of moving frames
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The analytic Carathéodory conjecture.
The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group.
The Area of the Generalized Gaussian Image and the Stability of Minimal Surfaces in Sn and IRn.
The area preserving curve shortening flow with Neumann free boundary conditions
We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.
The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces.
The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces.
The automorphism groups of finite type -structures on orbifolds.
The automorphism groups of foliations with transverse linear connection
The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.
The behaviour of the total twist and self-linking number of a closed space curve under inversions.
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 Bend of Bernstein Polynomials.
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 Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
It is proved that if is a weakly 1-complete Kähler manifold with only one end, then or there exists a proper holomorphic mapping of onto a Riemann surface.
The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.
The Bott Obstruction to the Existence of Nice Polarizations.
The bottleneck conjecture.
The bottom of the spectrum of a Riemannian covering.