Complete surfaces with negative extrinsic curvature

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dc.creatorSchlenker, Jean-Marc
dc.date1999-12-13
dc.date.accessioned2026-07-07T05:32:16Z
dc.date.available2026-07-07T05:32:16Z
dc.descriptionN. V. Efimov \cite{Ef1} proved that there is no complete, smooth surface in $\R^3$ with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if $M^3$ has sectional curvature between two constants $K_2$ and $K_3$, then there exists $K_1 < \min(K_2, 0)$ such that $M$ contains no smooth, complete immersed surface with curvature below $K_1$. Optimal values of $K_1$ are determined. This results rests on a phenomenon of propagations for degenerations of solutions of hyperbolic Monge-Amp{è}re equations.
dc.description38 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/9912101
dc.identifierhttp://arxiv.org/abs/math/9912101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79597
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C45; 58G16, 35L55
dc.titleComplete surfaces with negative extrinsic curvature
dc.typetext

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