Volume 19, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Simple Riemannian surfaces are scattering rigid

Haomin Wen

Geometry & Topology 19 (2015) 2329–2357
Abstract

Scattering rigidity of a Riemannian manifold allows one to recognize the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to recognize the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We will discuss the subtle difference between these two types of rigidities and prove that they are equivalent for two-dimensional simple manifolds with boundaries. In particular, this implies that two-dimensional simple manifolds (such as the flat disk) are scattering rigid since they are lens/boundary rigid.

Keywords
scattering rigidity, lens rigidity, knot
Mathematical Subject Classification 2010
Primary: 53C24
Secondary: 57M27
References
Publication
Received: 16 June 2014
Accepted: 5 October 2014
Published: 29 July 2015
Proposed: Dmitri Burago
Seconded: Tobias H Colding, Bruce Kleiner
Authors
Haomin Wen
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Germany
http://www.math.upenn.edu/~weh/