A characterization of revolution quadrics by a system of partial differential equations

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dc.creatorOliker, Vladimir
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:31:06Z
dc.date.available2026-07-07T12:31:06Z
dc.descriptionIt is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such solution its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in $\Rn$: paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.
dc.description7 pages, To appear in Proceedings of the AMS
dc.identifierhttps://arxiv.org/abs/0901.2508
dc.identifierhttp://arxiv.org/abs/0901.2508
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216338
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53A05, 53C40
dc.titleA characterization of revolution quadrics by a system of partial differential equations
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