Related papers: The copolarity of pseudo-cones

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…

We study some homological properties of the conductor ideal.

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stronger than might initially seem. We give some implications of…

We prove that small deformations of canonical singularities are canonical.

Every normal periodic tiling is a strongly balanced tiling. The properties of periodic tilings by convex polygons are rearranged from the knowledge of strongly balanced tilings. From the results, we show the properties of representative…

We prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body.

We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar…

We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In…

In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…

Families of translates and homothets of strictly convex curves are proven to possess Helly-type properties generalizing those of a circle. Weaker results are shown for arbitrary convex curves.

We introduce a new operation, copolar addition, on unbounded convex subsets of the positive orthant of real euclidean space and establish convexity of the covolumes of the corresponding convex combinations. The proof is based on a technique…

We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.

A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…

We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).

Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.

We show a reverse isoperimetric inequality within the class of relative outer parallel bodies, with respect to a general convex body $E$, along with its equality condition. Based on the convexity of the sequence of quermassintegrals of…

The similarities and differences between polariton condensation in microcavities and standard lasing in a semiconductor cavity structure are reviewed. The recent experiments on "photon condensation" are also reviewed.

We prove that various GIT semistabilities of polarized varieties imply semi-log-canonicity.