A Simple Proof of the Kinematic Formula.
A simpler construction of volume polynomials for a polyhedron.
A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls
Negative association for a family of random variables means that for any coordinatewise increasing functions f,g we have for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of...
A stability estimate for the Aleksandrow-Fnechel inequality, with an application to mean curvature.
A Stability Property of the Densest Circle Packing.
A stability theorem for the area sum of a convex polygon and its polar reciprocal.
A staircase illumination theorem for orthogonal polygons.
A study of variational inequalities for set-valued mappings.
A sufficient condition for the convexity of the area of an isoptic curve of an oval
A supplement to Eddy's paper.
A survey of Sylvester's problem and its generalizations.
A survey on local cohomology and 𝓓-modules
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...
A systematization of convexity concepts for sets and functions.
A theorem on nonexistence of a certain type of nearly regular cell-decompositions of the sphere
A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets.
A typical convex surface contains no closed geodesic.
A Unified Theory of Proportion
A Unified Theory of Proportion
A unified treatment of the theories of matroids with coefficients and of -matroids with coefficients.