Work

Dimension‐Independent Functional Inequalities by Tensorization and Projection Arguments

Year: 2026

Type: article

Abstract: ABSTRACT We study stability under tensorization and projection‐type operations of gradient estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation inequalities obtained by Baudoin and Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be dimension‐independent. Our results are applicable to hypoelliptic diffusions on sub‐Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension‐independent reverse Poincaré inequality, reverse logarithmic Sobolev inequality, and gradient bounds on Lie groups with transverse symmetries and for non‐isotropic Heisenberg groups.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70164

Authors: Fabrice Baudoin, Maria Gordina, Rohan Sarkar

Institutions: Aarhus University, University of Rochester, Binghamton University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Some topics in Analysis and Probability in Metric Measure Spaces, Random Matrices, and Diffusions, Asymptotics and ergodicity of hypoelliptic random processes, Probabilistic Methods in Analysis, Geometry, and Beyond