Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 149–178 | Cite as

Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds

  • François FillastreEmail author
  • Dmitriy Slutskiy


We prove that any metric of non-positive curvature in the sense of Alexandrov on a compact surface can be isometrically embedded as a convex spacelike Cauchy surface in a flat spacetime of dimension \((2+1).\) The proof follows from polyhedral approximation.


Alexandrov surfaces Convex surfaces Minkowski space Teichmüller space 

Mathematics Subject Classification

53C45 53B30 51M09 



The authors want to thank Giona Veronelli who pointed out an error in a preceding version of this text. Most of this work was achieved when the second author was a post-doc in the AGM institute of the Cergy-Pontoise University. He wants to thank the institution for its support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Cergy-PontoiseUMR CNRS 8088Cergy-PontoiseFrance

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