Search results for "Total curvature"

showing 5 items of 5 documents

Surfaces non-orientables de genre deux

1993

The existence of nonorientable complete minimal surface of genus two, one end and total curvature −2π(2n+3),n≥3 is proved in this paper.

CombinatoricsMinimal surfaceGeneral MathematicsGenus (mathematics)Total curvatureMathematicsBoletim da Sociedade Brasileira de Matem�tica
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On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

Convex analysisCombinatoricsFundamental theorem of curvesConvex polytopeConvex curveMathematical analysisConvex setTotal curvatureFour-vertex theoremGeometry and TopologyCurvatureMathematicsJournal of Geometry
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Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature

1974

Mean curvature flowMean curvatureGeneral MathematicsPrescribed scalar curvature problemMathematical analysisConstant-mean-curvature surfaceTotal curvatureSectional curvatureCurvatureScalar curvatureMathematicsMathematische Zeitschrift
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Hadamard-type theorems for hypersurfaces in hyperbolic spaces

2006

Abstract We prove that a bounded, complete hypersurface in hyperbolic space with normal curvatures greater than −1 is diffeomorphic to a sphere. The completeness condition is relaxed when the normal curvatures are bounded away from −1. The diffeomorphism is constructed via the Gauss map of some parallel hypersurface. We also give bounds for the total curvature of this parallel hypersurface.

Pure mathematicsGauss mapMathematics::Dynamical SystemsMathematics::Complex VariablesHyperbolic spaceSecond fundamental formMathematical analysisCauchy–Hadamard theoremGauss–Kronecker curvatureSecond fundamental formHypersurfaceMathematics::Algebraic GeometryComputational Theory and MathematicsBounded functionHadamard theoremTotal curvatureDiffeomorphismGeometry and TopologyMathematics::Differential GeometryAnalysisConvex hypersurfaceMathematicsDifferential Geometry and its Applications
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On bounds for total absolute curvature of surfaces in hyperbolic 3-space

2003

Abstract We construct examples of surfaces in hyperbolic space which do not satisfy the Chern–Lashof inequality (which holds for immersed surfaces in Euclidean space). To cite this article: R. Langevin, G. Solanes, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Surface (mathematics)Differential geometryEuclidean spaceHyperbolic spaceMathematical analysisHyperbolic manifoldTotal curvatureGeneral MedicineCurvatureHyperbolic triangleMathematicsComptes Rendus Mathematique
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