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Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
 
J. L. Flores University of Malaga, Malaga, Spain
J. Herrera University of Malaga, Malaga, Spain
M. Sánchez University of Granada, Granada, Spain
Front Cover for Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
Available Formats:
Electronic ISBN: 978-1-4704-1064-3
Product Code: MEMO/226/1064.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
Front Cover for Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
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  • Front Cover for Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
  • Back Cover for Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
J. L. Flores University of Malaga, Malaga, Spain
J. Herrera University of Malaga, Malaga, Spain
M. Sánchez University of Granada, Granada, Spain
Available Formats:
Electronic ISBN:  978-1-4704-1064-3
Product Code:  MEMO/226/1064.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2262013; 76 pp
    MSC: Primary 53; 83;

    Recently, the old notion of causal boundary for a spacetime \(V\) has been redefined consistently. The computation of this boundary \(\partial V\) on any standard conformally stationary spacetime \(V=\mathbb{R}\times M\), suggests a natural compactification \(M_B\) associated to any Riemannian metric on \(M\) or, more generally, to any Finslerian one. The corresponding boundary \(\partial_BM\) is constructed in terms of Busemann-type functions. Roughly, \(\partial_BM\) represents the set of all the directions in \(M\) including both, asymptotic and “finite” (or “incomplete”) directions.

    This Busemann boundary \(\partial_BM\) is related to two classical boundaries: the Cauchy boundary \(\partial_{C}M\) and the Gromov boundary \(\partial_GM\).

    The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification \(M_B\), relating it with the previous two completions, and (3) to give a full description of the causal boundary \(\partial V\) of any standard conformally stationary spacetime.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Cauchy completion of a generalized metric space
    • 4. Riemannian Gromov and Busemann completions
    • 5. Finslerian completions
    • 6. C-boundary of standard stationary spacetimes
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Volume: 2262013; 76 pp
MSC: Primary 53; 83;

Recently, the old notion of causal boundary for a spacetime \(V\) has been redefined consistently. The computation of this boundary \(\partial V\) on any standard conformally stationary spacetime \(V=\mathbb{R}\times M\), suggests a natural compactification \(M_B\) associated to any Riemannian metric on \(M\) or, more generally, to any Finslerian one. The corresponding boundary \(\partial_BM\) is constructed in terms of Busemann-type functions. Roughly, \(\partial_BM\) represents the set of all the directions in \(M\) including both, asymptotic and “finite” (or “incomplete”) directions.

This Busemann boundary \(\partial_BM\) is related to two classical boundaries: the Cauchy boundary \(\partial_{C}M\) and the Gromov boundary \(\partial_GM\).

The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification \(M_B\), relating it with the previous two completions, and (3) to give a full description of the causal boundary \(\partial V\) of any standard conformally stationary spacetime.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Cauchy completion of a generalized metric space
  • 4. Riemannian Gromov and Busemann completions
  • 5. Finslerian completions
  • 6. C-boundary of standard stationary spacetimes
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