Open Whitney umbrellas are locally polynomially convex

TL;DR

This paper proves that smooth open Whitney umbrellas in complex two-dimensional space are locally polynomially convex at their singular points, contributing to the understanding of their geometric structure.

Contribution

It establishes the local polynomial convexity of smooth open Whitney umbrellas in ^2 near singularities, a new result in complex geometry.

Findings

Open Whitney umbrellas are locally polynomially convex near singular points.

The result enhances understanding of singular Lagrangian surfaces in complex analysis.

Provides a foundation for further studies on the local geometry of singular surfaces.

Abstract

It is proved that any smooth open Whitney umbrella in $\mathbb C^2$ is locally polynomially convex near the singular point.