Related papers: Tangent hyperplanes to subriemannian balls

We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure.…

For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…

We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can improve…

We prove the existence of Gysin morphisms for hyperplane sections that may not satisfy the usual hypotheses of the Lefschetz hyperplane theorem. As an application, we show the triviality of the Alexander polynomial of a particular class of…

We examine the possibility of artificial Hawking radiation by proposing a non-PT - symmetric weakly pseudo-Hermitian two band model containing a tilting parameter. We also determine the tunneling probability using our Hamiltonian through…

We discuss certain kinds of diffusions on hyperbolic spaces, associated random walks on discrete groups of isometries of the latter, and their Martin boundaries.

We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.

This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds.

We compute the limit of tangents of an arbitrary surface. We obtain as a byproduct an embedded version of Jung's desingularization theorem for surface singularities with finite limits of tangents.

In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. More precisely, we prove that if a Euclidean ball is symplectically embedded in the…

Astrophysical models developed to explain superluminal motion in beaming phenomena are shown to be incomplete and the correct kinematical expression in any case to predict projected velocities slower than the speed of light. The observed…

The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple formulations, but rather intricate proofs. Related and still unsolved…

We extend the method of minimal vectors to arbitrary Banach spaces. It is proved, by a variant of the method, that certain quasinilpotent operators on arbitrary Banach spaces have hyperinvariant subspaces.

We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…

We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In…

We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a…

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.

We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…

We study a family of Riemannian problems on the Heisenberg group that tends to the sub-Riemannian problem on this group.

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…