Gromov Compactness in Hoelder Spaces and Minimal Connections on Jet Bundles

TL;DR

This paper proves Gromov convergence in Hoelder spaces for curves with totally real boundary conditions, utilizing reflection principles and jet bundle connections to achieve higher regularity and boundary estimates.

Contribution

It introduces a novel proof of Gromov compactness in Hoelder spaces for boundary value problems using reflection principles and jet bundle techniques.

Findings

Established Gromov convergence in Hoelder spaces for curves with boundary.

Developed boundary regularity estimates using reflection principles.

Connected jet bundle connections with Gromov compactness results.

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.