A note on pseudoconvex hypersurfaces of infinite type in $\mathbb C^n$

TL;DR

This paper constructs a smooth pseudoconvex hypersurface of infinite type in complex space that admits no holomorphic curves tangent to it to infinite order, challenging previous assumptions about such hypersurfaces.

Contribution

It provides an example of a pseudoconvex hypersurface of infinite type without tangent holomorphic curves, revealing new geometric properties.

Findings

Existence of a pseudoconvex hypersurface with no tangent holomorphic curves

Counterexample to previous conjectures about infinite type hypersurfaces

Insight into the geometry of pseudoconvex hypersurfaces

Abstract

The purpose of this article is to prove that there exists a real smooth pseudoconvex hypersurface germ $(M,p)$ of D'Angelo infinite type in $\mathbb C^{n+1}$ such that it does not admit any (singular) holomorphic curve in $\mathbb C^{n+1}$ tangent to $M$ at $p$ to infinite order.