Let S be an ordered set of disjoint unit spheres in R. We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the entire family has a line transversal. Without the order condition, we show that the existence of a line transversal for every subset of at most 11 spheres from S implies the existence of a line transversal for S.

We prove Helly-type theorems for line transversals to disjoint unit balls in R. In particular, we show that a family of n > 2d disjoint unit balls in R has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n > 4d − 1 disjoint unit balls in R admits a line transversal if any subfamily of ...

We introduce a method to bound attractors of dissipative dynamical systems in phase and parameter spaces. The method is based on the determination of families of transversal surfaces (surfaces crossed by the flow in only one direction). This technique yields very restrictive geometric bounds in phase space for the attractors. It also gives ranges of parameters of the system for which no chaotic...

Light-cone gauge quantization procedures are given, for superstring theory on AdS3 space charged with NS-NS background, both in NSR and GS formalism. The spacetime (super)conformal algebras are constructed in terms of the transversal physical degrees of freedom. The spacetime conformal anomaly agrees with that of covariant formalism, provided that the worldsheet conformal anomaly c equals 26 or...

A linear partial spread is a set of mutually skew lines of some P(V ) – where V is a finite dimensional vector space over a field – that are characterized by the property that their images under the Plücker embedding are in a given subspace of P (∧2 V ); it is a linear spread if the lines in it cover the whole space. We will provide methods to construct linear partial spreads, and characterize ...

INTRODUCTION Let F be a family of convex sets in R. A geometric transversal is an affine subspace that intersects every member of F . More specifically, for a given integer 0 ≤ k < d, a k-dimensional affine subspace that intersects every member of F is called a ktransversal to F . Typically, we are interested in necessary and sufficient conditions that guarantee the existence of a k-transversal...

INTRODUCTION Let F be a family of convex sets in R. A geometric transversal is an affine subspace that intersects every member of F . More specifically, for a given integer 0 ≤ k < d, a k-dimensional affine subspace that intersects every member of F is called a ktransversal to F . Typically, we are interested in necessary and sufficient conditions that guarantee the existence of a k-transversal...

In this note we show that Tolman’s example (of a six dimensional Hamiltonian T -space with isolated fixed points and no compatible Kähler structure) can be constructed from the flag variety U(3)/U(1) by U(2)-equivariant symplectic surgery. This implies that Tolman’s space has a “transversal multiplicity-free” action of U(2) and that Delzant’s theorem “every compact multiplicity-free torus actio...

A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy. A measured solenoid immersed in a smooth manifold produces a closed current (known as a generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (up to scalars) transversal measure. It is known that for any smooth manifold, any real homology class is re...

(λk(u), rk(u) being the k-th eigenvalue and a corresponding eigenvector of A(u)) is either the whole space or consists of a finite number of smooth, N−1dimensional, connected, manifolds that are transversal to the characteristic vector field rk. Relying on an adapted wave tracing method, we obtain the same tipe of error estimates valid for hyperbolic systems satisfying the classical assumptions...