Near geodesics in John domains in Banach spaces

Abstract

Let $E$ be a real Banach space with dimension at least 2. In this paper, we prove that if $D\subset E$ is a John domain which is homeomorphic to an inner uniform domain via a CQH map, then each neargeodesic in $D$ is a cone arc.

revised in IJM. arXiv admin note: text overlap with arXiv:1104.5128, arXiv:1206.0128 by other authors

References in corpus (2)

• Quasihyperbolic Geometry in Euclidean and Banach Spaces
• The quasiconformal subinvariance property of John domains in $\protect \IR^n$ and its application