Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …

This survey is devoted to some results in the area of combinatorial and convex geometry,
from classical theorems up to the latest contemporary results, mainly those results whose …

A problem is solved or some other goal achieved by “topological methods” if in our
arguments we appeal to the “form,” the “shape,” the “global” rather than “local” structure of …

An old problem in combinatorial geometry is to determine when one or more measurable
sets in Rd admit an equipartition by a collection of k hyperplanes [B. Grünbaum, Partitions of …

A conical dissection of R d is a decomposition of the space into polyhedral cones. An
example of a conical dissection is a fan associated to the faces of a convex polytope …

The conclusion of the classical ham sandwich theorem for bounded Borel sets may be
strengthened, without additional hypotheses–there always exists a common bisecting …

The problem of the existence of an equivariant map is a classical topological problem
ubiquitous in topology and its applications. Many problems in discrete geometry and …

Applications of harmonic analysis on finite groups are introduced to measure partition
problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For …

Abstract Equivariant Ham Sandwich Theorems are obtained for the classical algebras F= R,
C, and H and the finite subgroups G of their unit spheres. Given any n F-valued Borel …

Dold's theorem gives sufficient conditions for proving that there is no G-equivariant mapping
between two spaces. We prove a generalization of Dold's theorem, which requires triviality …