Work

Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension

Year: 2026

Type: article

Abstract: We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to the setting of intermediate dimensions both the Gehring–Väisälä theorem on dilatation‐dependent quasiconformal distortion of dimension and Kovalev's theorem on the nonexistence of metric spaces with conformal dimension strictly between zero and one. Applications include new contributions to the quasiconformal classification of Euclidean sets and a new sufficient condition for the vanishing of conformal box‐counting dimension. We illustrate our conclusions with specific consequences for Bedford–McMullen carpets, samples of Mandelbrot percolation, and product sets containing a polynomially convergent sequence factor.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70445

Authors: Jonathan M. Fraser, Jeremy T. Tyson

Institutions: University of St Andrews, University of Illinois Urbana-Champaign

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Simons Foundation, Leverhulme Trust, University of St Andrews, Engineering and Physical Sciences Research Council