Hölder maps from Euclidean spaces to Carnot groups

2025/08/22 by Balogh, Zoltan, Kozhevnikov, Artem, Pansu, Pierre
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2508.16180

Abstract

We give alternative proofs of (unsharp) results of Gromov's on his H''older equivalence problem: for which α does there exist a C^α-homeomorphism of an open set of Euclidean space to an open set of a given Carnot group? We indicate a possible route to sharp bounds.

Citations

• Submanifolds and differential forms on Carnot manifolds, after M. Gromov and M. Rumin
• Some properties of Hölder surfaces in the Heisenberg group

Related

• A variant of Gromov's problem on Hölder equivalence of Carnot groups
• Constructing Hölder maps to Carnot groups
• On the quasisymmetric Hölder-equivalence problem for Carnot groups
• Geometry of Carnot--Carathéodory Spaces, Differentiability and Coarea Formula
• Reshetnyak-class mappings and composition operators