Geometry & Topology Volume 19, issue 4 (2015)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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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