Uniqueness of starshaped compact hypersurfaces with prescribed $m$-th mean curvature in hyperbolic space

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dc.creatorBarbosa, J. Lucas M.
dc.creatorde Lira, Jorge H. S.
dc.creatorOliker, Vladimir
dc.date2007-02-25
dc.date.accessioned2026-07-07T07:48:49Z
dc.date.available2026-07-07T07:48:49Z
dc.descriptionLet $ψ$ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface $M$ for which $ψ$, when evaluated on $M$, coincides with the $m-$th elementary symmetric function of principal curvatures of $M$ for a given $m$? The corresponding existence and uniqueness problems in Euclidean space have been investigated by several authors in the mid 1980's. Recently, conditions for existence were established in elliptic space and, most recently, for hyperbolic space. However, the uniqueness problem has remained open. In this paper we investigate the problem of uniqueness in hyperbolic space and show that uniqueness (up to a geometrically trivial transformation) holds under the same conditions under which existence was established.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0702750
dc.identifierhttp://arxiv.org/abs/math/0702750
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124631
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53A10, 35J60
dc.titleUniqueness of starshaped compact hypersurfaces with prescribed $m$-th mean curvature in hyperbolic space
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