3 papers
math.AP2025
Contractive transport maps from to nearly spherical surfaces with positive Ricci curvature
Jordan Serres
We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow o…
math.AP2024
Isoperimetric and geometric inequalities in quantitative form: Stein's method approach
Jordan Serres
We adapt Stein's method to isoperimetric and geometric inequalities. The main challenge is the treatment of boundary terms. We address this by using an elliptic PDE with an oblique…
math.FA2024
Generalized perimeters and gradient estimates
Jordan Serres
We use a variational formulation to define a generalized notion of perimeter, from which we derive abstract isoperimetric Cheeger's inequalities via gradient estimates on solutions…