Geometry & Topology Volume 19, issue 4 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Other MSP Journals

Simple Riemannian surfaces are scattering rigid

Haomin Wen

Geometry & Topology 19 (2015) 2329–2357

DOI: 10.2140/gt.2015.19.2329

Bibliography

1	S B Alexander, I D Berg, R L Bishop, The Riemannian obstacle problem, Illinois J. Math. 31 (1987) 167 MR869484
2	G Besson, G Courtois, S Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (1995) 731 MR1354289
3	D Burago, S Ivanov, Boundary rigidity and filling volume minimality of metrics close to a flat one, Ann. of Math. 171 (2010) 1183 MR2630062
4	D Burago, S Ivanov, Area minimizers and boundary rigidity of almost hyperbolic metrics, Duke Math. J. 162 (2013) 1205 MR3079248
5	S Chmutov, V Goryunov, H Murakami, Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves, Math. Ann. 317 (2000) 389 MR1776110
6	C B Croke, Scattering rigidity with trapped geodesics, Ergodic Theory Dynam. Systems 34 (2014) 826 MR3199795
7	C B Croke, B Kleiner, A rigidity theorem for simply connected manifolds without conjugate points, Ergodic Theory Dynam. Systems 18 (1998) 807 MR1645381
8	J Eaton, On spherically symmetric lenses, IRE Trans. Antennas Propa. AP-4 (1952) 66
9	D B A Epstein, Curves on $2$–manifolds and isotopies, Acta Math. 115 (1966) 83 MR0214087
10	M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
11	J H Hannay, T M Haeusser, Retroreflection by refraction, J. Modern Opt. 40 (1993) 1437 MR1232761
12	A Hatcher, Notes on basic $3$–manifold topology (2000)
13	M Kerker, The scattering of light and other electromagnetic radiation, Academic Press (1969)
14	R Michel, Sur la rigidité imposée par la longueur des géodésiques, Invent. Math. 65 (1981/82) 71 MR636880
15	L Pestov, G Uhlmann, Two-dimensional compact simple Riemannian manifolds are boundary distance rigid, Ann. of Math. 161 (2005) 1093 MR2153407