Higher order invariants of Levi degenerate hypersurfaces

TL;DR

This paper studies higher order CR invariants of three-dimensional hypersurfaces, providing classifications based on automorphism groups, and explores conditions for local convexifiability of pseudoconvex hypersurfaces in higher dimensions.

Contribution

It offers a complete normal form characterization for hypersurfaces with trivial automorphism groups and establishes necessary conditions for convexifiability in higher dimensions.

Findings

Complete classification of hypersurfaces with trivial automorphism groups

Normal form characterization for finite automorphism groups

Necessary condition for local convexifiability in higher dimensions

Abstract

The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and analogous results for finite groups. The second part considers hypersurfaces of finite Catlin multitype and the Kohn-Nirenberg phenomenon in higher dimensions. We give a necessary condition for local convexifiability of a class of pseudoconvex hypersurfaces in $\mathbb C^{n+1}$.