2018-03-162018-02-26MENDEZ, Milton Javier Cárdenas. Parametrização de uma hipersuperfície via função suporte no espaço hiperbólico. 2018. 77 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.http://repositorio.bc.ufg.br/tede/handle/tede/8225First objective will revise the hyperbolic Gauss map for hypersurfaces Mn C Hn+1 and its relation with tangent horospheres. We will introduce horospherical ovaloids as compact hypersurfaces with regular hyperbolic Gauss map and analyze their properties, analyzes the possible formulations of the Christoffel problem in Hn+1 and that this leads to the notion of hyperbolic curvature radii. Second objective we will prove that the Nirenberg problem on Sn is equivalent to the Christoffel problem in Hn+1. This equivalence is made explicit by means of a representation formula for hypersurfaces in terms of the hyperbolic Gauss map and the horospherical support function.application/pdfAcesso AbertoProblema de ChristoffelProblema de NirenbergHoroesferasMétrica horoesfericaRaio de curvatura hiperbólicoAplicação hiperbólica de GaussChristoffel problemNirenberg problemHorospheresHorospherical metricHyperbolic curvature radiiHyperbolic Gauss mapCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação