• Title/Summary/Keyword: Lorentzian Gromov-Hausdorff theory

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ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE

  • Yun, Jong-Gug
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.957-964
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    • 2014
  • In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($M_{\alpha},d_{\alpha}$)} of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_{\alpha}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($M_{\alpha},d_{\alpha}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.