Communications in Analysis and Geometry

Volume 29 (2021)

Number 1

Regularity of CR-mappings of codimension $1$ into Levi-degenerate hypersurfaces

Pages: 151 – 181



Ilya Kossovskiy (Department of Mathematics, Masaryk University, Brno, Czech Republic)

Bernhard Lamel (Department of Mathematics, University of Vienna, Austria)

Ming Xiao (Department of Mathematics, University of California at San Diego, La Jolla, Calif., U.S.A.)


We provide regularity results for CR-maps from a real hypersurface in $n$-dimensional complex space to a Levi-degenerate target hypersurface in a $n + 1$-dimensional space. We address both the real-analytic and the smooth case. Our results allow immediate applications to the study of proper holomorphic maps between Bounded Symmetric Domains.

Received 28 March 2017

Accepted 15 April 2018

Published 11 March 2021