2018/08/25 by Michael Christ, Christ, Michael, Marina Iliopoulou +1
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1808.08368
openalex publication_date 2018/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A version of the Riesz-Sobolev convolution inequality is formulated and proved for arbitrary compact connected Abelian groups. Maximizers are characterized and a quantitative stability theorem is proved, under natural hypotheses. A corresponding stability theorem for sets whose sumset has nearly minimal measure is also proved, sharpening recent results of other authors. For the special case of the group ℝ/ℤ, a continuous deformation of sets is developed, under which an appropriately scaled Riesz-Sobolev functional is shown to be nondecreasing.