We prove a sharp stability result concerning how close homothetic sets attaining near-equality in the Brunn–Minkowski inequality are to being convex. In particular, resolving conjecture of Figalli and Jerison, we show there universal constants $\\smash{C_n,d_n>0}$ such that for $\\smash{A \\subset \\mathbb{R}^n}$ positive measure, if $\\smash{|\\frac{A+A}{2}\\setminus A| \\le d_n |A|}$, then $\...

This paper develops a formula for the equivariant chain-complex of the universal covering space of a Serre bration's total space in terms of equivariant chain-complexes of the base and ber. The present paper's distinguishing feature is that both the base and ber are allowed to be non-simply-connected: the fundamental group of the total space is thus an extension of that of the base by that of t...

We investigate analytic properties of height zeta functions of toric bundles over flag varieties.

We will prove a result concerning the inclusion of non-trivial invariant ideals inside nontrivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on C∗-algebras. The motivation of this study is our recent research on C-unique groups (or Fourier groups) in [10]. In fact, one in...

Given a group G and an endomorphism ? of G, two elements x,y?G are said to be ?-conjugate if x=gy?(g)?1 for some g?G. The number equivalence classes this relation is the Reidemeister R(?) ?. set {R(?)|??Aut(G)} called spectrum G. We investigate numbers spectra on direct products finitely many groups determine what information can derived from individual factors.