A new proof of the C^∞ regularity of C² conformal mappings on the Heisenberg group

2017/01/11 by Alex D. Austin, Austin, Alex D., Jeremy T. Tyson +1
Mathematics · #30C35 #35H10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #msc:30C35 #msc:35H10

paper · pdf · doi:10.48550/arxiv.1701.03182

10 pages

arxiv created 2017/01/11 · openalex publication_date 2017/01/11 · arxiv updated 2017/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof for the C^∞ regularity of C² smooth conformal mappings of the sub-Riemannian Heisenberg group. Our proof avoids any use of nonlinear potential theory and relies only on hypoellipticity of Hörmander operators and quasiconformal flows. This approach is inspired by prior work of Sarvas and Liu.

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