Morse Quasiflats II

Abstract

This is the second in a two part series of papers concerning Morse quasiflats - higher dimensional analogs of Morse quasigeodesics. Our focus here is on their asymptotic structure. In metric spaces with convex geodesic bicombings, we prove asymptotic conicality, uniqueness of tangent cones at infinity and Euclidean volume growth rigidity for Morse quasiflats. Moreover, we provide some immediate consequences.Comment: This paper and "Morse quasiflat I" were originally posted as a single paper arXiv:1911.04656v1. We have added several new results and rewritten the proof of the main theorem to improve readability. v2: minor corrections. v3: many modifications in the introduction, add a more detailed discussion of proofs with pictures in Section 4, add a short appendix on quasi-isometric classification. 3 Figure