Work

Stability of isoperimetric and Sobolev inequalities for excluded exponents on Riemannian manifolds

Year: 2026

Type: article

Abstract: Quasi-isometries are a versatile type of maps that preserve the large-scale geometry of spaces, while introducing significant local distortions. Following Kanai’s work, which established the invariance of various analytic and geometric properties under quasi-isometries, this paper generalizes isoperimetric and Sobolev inequalities for exponents less than the manifold’s dimension, proving both that they are equivalent and preserved by quasi-isometries.

Source: Revista Matemática Complutense

DOI: 10.1007/s13163-026-00571-x

Authors: Ana Granados, Ana Portilla, José M. Rodríguez, Eva Tourís

Institutions: Saint Louis University, Universidad Carlos III de Madrid, Universidad Autónoma de Madrid

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Universidad Autónoma de Madrid