Geodesic
Convex surfaces in Hyperbolic space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 278-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is concerned with complete, immersed generic hypersurfaces in a Hyperbolic space $L^n$, where $n>3$. Such surface, which is locally convex and locally supported by horosphere either compact, which is homeomorphic to a sphere or horosphere. 
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     author = {A. A. Borisenko and D. I. Vlasenko},
     title = {Convex surfaces in {Hyperbolic} space},
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A. A. Borisenko; D. I. Vlasenko. Convex surfaces in Hyperbolic space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 278-285. http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a1/