Geodesic
Simple Riemannian surfaces are scattering rigid
Wen, Haomin1
1 Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Geometry & topology, Tome 19 (2015) no. 4, pp. 2329-2357.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2015.19.2329
Classification : 53C24, 57M27
Keywords: scattering rigidity, lens rigidity, knot

Wen, Haomin 1

1 Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany 
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Wen, Haomin. Simple Riemannian surfaces are scattering rigid. Geometry & topology, Tome 19 (2015) no. 4, pp. 2329-2357. doi : 10.2140/gt.2015.19.2329. http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.2329/

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