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 $\...

In this paper, we consider the problem of constrained tracking of piecewise constant references for nonlinear dynamical systems. In the considered problem we assume that an existing controller satisfies constraints in a corresponding positive-invariant set of the system. To solve the problem we propose the use of homothetic transformations of the positive-invariant set to modify the existing co...

on a finsler manifold, we define conformal vector fields and their complete lifts and prove that incertain conditions they are homothetic.