Regularity of mappings into classical domains

We study the regularity and algebraicity for mappings into classical domains. Among other things, we establish everywhere regularity and algebraicity results for C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document} CR maps into the set of smooth boundary points of a classical domain where the codimension can be arbitrarily large.