Analytic continuation of holonomy germs of Riccati foliations along Brownian paths

TL;DR

This paper proves that holonomy germs of certain Riccati foliations on the complex projective plane can be analytically continued along generic Brownian paths, advancing understanding of foliation dynamics and stochastic processes.

Contribution

It establishes the analytic continuation of holonomy germs along Brownian paths for quasi-minimal Riccati foliations, a novel result linking stochastic analysis and complex foliation theory.

Findings

Holonomy germs can be analytically continued along Brownian paths.

The result applies to quasi-minimal Riccati foliations on the complex projective plane.

This links stochastic processes with complex foliation dynamics.

Abstract

This paper deals with the question of analytic continuation of holonomy germs of holomorphic foliations. We prove that for a quasi-minimal Riccati foliation of the complex projective plane, any holonomy germ of the foliation between complex projective lines can be analytically continued along a generic Brownian path.