Asymptotic behavior of flat surfaces in hyperbolic 3-space
KOKUBU, Masatoshi ; ROSSMAN, Wayne ; UMEHARA, Masaaki ; YAMADA, Kotaro
J. Math. Soc. Japan, Tome 61 (2009) no. 3, p. 799-852 / Harvested from Project Euclid
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In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic $3$ -space $H^{3}$ . Gálvez, Martínez and Milán showed that when the singular set does not accumulate at an end, the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that the asymptotic order (called pitch $p$ ) of the end determines the limiting shape, even when the singular set does accumulate at the end. If the singular set is bounded away from the end, we have $-1
Publié le : 2009-07-15
Classification:  flat surface,  flat front,  end,  asymptotic behavior,  hyperbolic 3-space,  53C42,  53A35 
@article{1248961479,
     author = {KOKUBU, Masatoshi and ROSSMAN, Wayne and UMEHARA, Masaaki and YAMADA, Kotaro},
     title = {Asymptotic behavior of flat surfaces in hyperbolic 3-space},
     journal = {J. Math. Soc. Japan},
     volume = {61},
     number = {3},
     year = {2009},
     pages = { 799-852},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1248961479}
}

KOKUBU, Masatoshi; ROSSMAN, Wayne; UMEHARA, Masaaki; YAMADA, Kotaro. Asymptotic behavior of flat surfaces in hyperbolic 3-space. J. Math. Soc. Japan, Tome 61 (2009) no. 3, pp.  799-852. http://gdmltest.u-ga.fr/item/1248961479/