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On compactification of Minkowski space and complex analysis in the future tube. (Russian) Zbl 0602.32010

Let \(\tau^+:=\{\zeta \in {\mathbb{C}}^ 4: (Im \zeta_ 0)^ 2 > (Im \zeta_ 1)^ 2+ (Im \zeta_ 2)^ 2+ (Im \zeta_ 3)^ 2\), Im \(\zeta\) \({}_ 0>0\}\) be a future tube. It is very important for mathematical physics [see the first author, ”Methods of the theory of functions of many complex variables”, (Russian) (1964; Zbl 0125.319); (English translation, Cambridge Mass. 1966)]. The authors study the topology of conformal compactification of Minkowski space (in Chapter 1) [see also R. Penrose, Proc. R. Sci. London, Ser. A 284, 159-203 (1965; Zbl 0129.412)] and consider a case when a distinguished boundary of \(\tau^+\) is a Minkowski space. In Chapter 2 it is proved that the domain \(\tau^+\) is not even locally pseudoconvex polyhedra [for \(n=3\) see the second author, Theor. Math. Phys. 54, 62-70 (1983); translation from Teor. Mat. Fiz. 54, No.1, 99-110 (1983; Zbl 0529.32001)]. In the third part the authors prove some theorems about the boundary properties of the holomorphic function in the future tube. [For the collection see also the second author, Izv. Akad. Nauk SSSR, Ser. Mat. 50, 1241-1275 (1986)].
Reviewer: M.Marinov

MSC:

32J05 Compactification of analytic spaces
32M99 Complex spaces with a group of automorphisms
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
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