Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds
著者
書誌事項
Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds
（Memoirs of the American Mathematical Society, no. 1064）
American Mathematical Society, c2013
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注記
"November 2013, volume 226, number 1064 (fifth of 5 numbers)."
Includes bibliographical references (p. 75-76)
内容説明・目次
内容説明
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 generalised (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.
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