Gromov Compactness in Hoelder Spaces and Minimal Connections on Jet Bundles

Abstract

The goal of this work is to establish a proof of the Gromov convergence in Hoelder spaces for curves with a totally real boundary condition following the original geometric idea of Gromov. We use a local reflection principle in neighbourhoods of the totally real submanifold as developed by Ivashkovich and Shevchishin and existence results for special connections on spaces of jet bundles to obtain higher regularity and Gromov-Schwarz estimates along the boundary.