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

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
This article is available for purchase or by subscription. See below.
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 $2$.

## PDF Access Denied

We have not been able to recognize your IP address 3.238.250.73 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

##### Keywords
symmetric spaces, quasi-isometries, coarse geometry, rigidity
##### Mathematical Subject Classification 2010
Primary: 22E40, 53C24, 53C35
##### Publication
Received: 24 May 2017
Revised: 14 January 2018
Accepted: 4 March 2018
Published: 1 June 2018
Proposed: Bruce Kleiner
Seconded: Martin Bridson, Anna Wienhard
##### Authors
 David Fisher Department of Mathematics Indiana University Bloomington, IN United States Kevin Whyte Department of Mathematics University of Illinois at Chicago Chicago, IL United States