Displaying similar documents to “Contractive curves.”

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

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In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary ∂ M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into ∂ M . We prove a result on filling S 2 by holomorphic discs.

On continuous solutions to linear hyperbolic systems

Małgorzata Zdanowicz, Zbigniew Peradzyński (2005)

Annales Polonici Mathematici

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We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.

Short separating geodesics for multiply connected domains

Mark Comerford (2011)

Open Mathematics

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We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We...

The Carathéodory topology for multiply connected domains II

Mark Comerford (2014)

Open Mathematics

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We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result...