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Boundary and lens rigidity of Lorentzian surfaces
KTH, Superseded Departments, Mathematics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-9184-1467
1996 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 348, 2307-2329 p.Article in journal (Refereed) Published
Abstract [en]

Let g be a Lorentzian metric on the plane ℝ2 that agrees with the standard metric g0 = -dx2 + dy2 outside a compact set and so that there are no conjugate points along any time-like geodesic of (ℝ2, g). Then (ℝ2, g) and (ℝ2, g0) are isometric. Further, if (M*, g*) and (M*, p*) are two dimensional compact time oriented Lorentzian manifolds with space-like boundaries and so that all time-like geodesies of (M, g) maximize the distances between their points and (M, g) and (M*, g*) are "boundary isometric", then there is a conformal diffeomorphism between (M, g) and (M*, g*) and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

Place, publisher, year, edition, pages
1996. Vol. 348, 2307-2329 p.
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URN: urn:nbn:se:kth:diva-47745DOI: 10.1090/S0002-9947-96-01688-1OAI: diva2:456092
QC 20111114. Available from: 2011-11-12 Created: 2011-11-12 Last updated: 2011-11-14Bibliographically approved

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