#### Volume 22, issue 5 (2018)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Quasi-isometric embeddings of symmetric spaces

### David Fisher and Kevin Whyte

Geometry & Topology 22 (2018) 3049–3082
##### Abstract

This paper opens the study of quasi-isometric embeddings of symmetric spaces. The main focus is on the case of equal and higher rank. In this context some expected rigidity survives, but some surprising examples also exist. In particular there exist quasi-isometric embeddings between spaces $X$ and $Y$ where there is no isometric embedding of $X$ into $Y\phantom{\rule{0.3em}{0ex}}$. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow–Morse lemma in higher rank. Typically this lemma is replaced by the quasiflat theorem, which says that the maximal quasiflat is within bounded distance of a finite union of flats. We improve this by showing that the quasiflat is in fact flat off of a subset of codimension $2$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/gt

We have not been able to recognize your IP address 34.239.158.107 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

##### Keywords
symmetric spaces, quasi-isometries, coarse geometry, rigidity
##### Mathematical Subject Classification 2010
Primary: 22E40, 53C24, 53C35