Related papers: Tangent hyperplanes to subriemannian balls
We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…
We provide a resolution of the Heesch problem for homogeneous (also known as semi-regular) tilings, and as a corollary, for tilings by convex monotiles in the hyperbolic plane. We also provide the first known example of weakly aperiodic…
Various objections against Alcubierre's warp drive geometry are reviewed. Superluminal warp bubbles seem an unlikey possibility within the framework of general relativity and quantum field theory, although subluminal bubbles may still be…
We introduce variational problems on Riemannian manifolds with constrained acceleration and derive necessary conditions for normal extremals in the constrained variational problem. The problem consists on minimizing a higher-order energy…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
Quantum tunneling from a thin wire or a thin film through a static potential barrier in a zero magnetic field is studied. The wire or the film should satisfy a condition of transverse quantization of levels and be inhomogeneous. Depending…
For a pseudoconvex tube domain, we prove estimates that relate the sublevel sets of its diagonal Bergman kernel to the floating bodies of its convex base. This allows us to associate a new affine invariant to any convex body.
In contrast to the classical twistor spaces whose fibres are 2-spheres, we introduce twistor spaces over manifolds with almost quaternionic structures of the second kind in the sense of P. Libermann whose fibres are hyperbolic planes. We…
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
We show that connected graphs admit sublinear longest path transversals. This improves an earlier result of Rautenbach and Sereni and is related to the fifty-year-old question of whether connected graphs admit longest path transversals of…
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the…
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some Estimates of the growth of the Lelong functions associated to the current and to its…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…
We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive…
We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.