Related papers: Intersection Bodies with Certain Symmetries
Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson…
In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of…
In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex…
We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
The intrinsic volumes of a convex body are fundamental invariants that capture information about the average volume of the projection of the convex body onto a random subspace of fixed dimension. The intrinsic volumes also play a central…
The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…
It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent…
In this work, we study convex bodies in $\RR^{2n}$ with the property that their mean width cannot be infinitesimally decreased by symplectomorphisms. The common theme of our results is that toric symmetry is a preferred feature of convex…
A centrally symmetric convex body is a convex compact set with non-empty interior that is symmetric about the origin. Of particular interest are those that are both smooth and strictly convex -- known here as regular symmetric bodies --…
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…
We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex bodies.
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…
A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of…
In the context of classical or quantum many-body problems involving identical bodies, a linear change of coordinates can be constructed with the properties that it includes the center-of-mass as one of the new coordinates and preserves the…
This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…