Morse Quasiflats I
Abstract
This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate assumptions on the ambient space we show that they are equivalent and quasi-isometry invariant; we also give a variety of examples. The second paper proves that Morse quasiflats are asymptotically conical and have canonically defined Tits boundaries; it also gives some first applications.
Keywords
Cite
@article{arxiv.1911.04656,
title = {Morse Quasiflats I},
author = {Jingyin Huang and Bruce Kleiner and Stephan Stadler},
journal= {arXiv preprint arXiv:1911.04656},
year = {2021}
}
Comments
Version 1 of this posting, which was called "Morse quasiflats", has been split into two parts -- "Morse quasiflats I", which is Version 2 of this posting, and "Morse quasiflats II", which is posted as arXiv:2003.08912. We add several new results and rewrite several places to improve readability. v3: minor corrections. v4: many modifications in light of the referee's comments, accepted version