Analytic filling of totally real tori

TL;DR

This paper proves that under certain conditions, analytic discs attached to totally real tori in complex space can be extended to fill the space analytically, advancing understanding in complex geometry and symplectic topology.

Contribution

It establishes a new extension result for analytic discs attached to totally real tori within specific geometric conditions.

Findings

Analytic discs of Maslov index two can be extended to fill the space.

Extension is possible when the torus lies in a regular level set of a strictly plurisubharmonic function.

Provides new insights into the structure of totally real tori in complex spaces.

Abstract

We prove that any embedded Maslov index two analytic disc attached to a totally real torus in the complex two-dimensional affine space extends to an analytic filling provided that the torus is contained in a regular level set of a strictly plurisubharmonic function.