Riemann surfaces and totally real tori
Julien Duval, Damien Gayet
TL;DR
This paper investigates the properties of totally real tori in the complex plane, establishing an either-or condition related to holomorphic fillings and rational convexity.
Contribution
It introduces a new dichotomy for totally real tori in the complex plane, linking holomorphic fillings with rational hull properties.
Findings
Either the torus admits a holomorphic filling and is rationally convex.
Or its rational hull contains a holomorphic annulus.
Abstract
Given a generic totally real torus unknotted in the unit sphere of the complex plane, we prove the following alternative : either there exists a filling of the torus by holomorphic discs and the torus is rationally convex, or its rational hull contains a holomorphic annulus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Geometry and complex manifolds