Boundary and Lens Rigidity of Lorentzian Surfaces |
| |
| Authors: | Lars Andersson Mattias Dahl Ralph Howard |
| |
| Affiliation: | Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden ; Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden ; Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208 |
| |
| Abstract: | Let  be a Lorentzian metric on the plane  that agrees with the standard metric  outside a compact set and so that there are no conjugate points along any time-like geodesic of  . Then  and  are isometric. Further, if  and  are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of  maximize the distances between their points and  and  are ``boundary isometric', then there is a conformal diffeomorphism between  and  and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds. |
| |
| Keywords: | |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Transactions of the American Mathematical Society》下载全文 |
|
