A sphericity criterion for strictly pseudoconvex hyper surfaces in $\mathbb{C}^2$ via invariant curves

TL;DR

This paper establishes a criterion for identifying when a strictly pseudoconvex hypersurface in ^2 is locally spherical, based on the behavior of chains and stationary discs.

Contribution

It introduces a sphericity criterion linking chains on hypersurfaces to stationary discs, providing a new geometric characterization.

Findings

If every chain coincides with the boundary of a stationary disc, then the hypersurface is locally spherical.

The paper characterizes local sphericity through invariant geometric structures.

Provides a new method to identify sphericity in complex hypersurfaces.

Abstract

We prove that if every chain on a strictly pseudoconvex hypersurface $M$ in $\mathbb{C}^2$ coincides with the boundary of a stationary disc, then $M$ is locally spherical.