共查询到20条相似文献,搜索用时 0 毫秒
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Wayne Rossman 《Journal of Geometric Analysis》2001,11(4):669-692
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature
1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces
in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number
of examples. 相似文献
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Francis E. Burstall Udo Hertrich-Jeromin Wayne Rossman 《Comptes Rendus Mathematique》2010,348(11-12):661-664
We propose a Lie geometric point of view on flat fronts in hyperbolic space as special Ω-surfaces and discuss the Lie geometric deformation of flat fronts. 相似文献
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We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H~3 found by Mori(1981), we obtain 2-and 3-parameter families of new minimal surfaces in the hyperbolic space, by solving a non trivial integro-differential system. Special choices of the parameters provide minimal surfaces whose parametrizations are defined on connected regions of R~2 minus a disjoint union of Jordan curves. Any connected region bounded by such a Jordan curve, generates a complete minimal surface, whose boundary at infinity of H~3 is a closed curve. The geometric properties of the surfaces regarding the ends, completeness and symmetries are discussed. 相似文献
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Alberto Candel 《Transactions of the American Mathematical Society》2007,359(8):3567-3575
This paper gives an upper bound for the first eigenvalue of the universal cover of a complete, stable minimal surface in hyperbolic space, and a sharper one for least area disks.
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《Mathematische Nachrichten》2017,290(4):570-582
The contribution of this paper is two‐fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing vector field, by considering the Busemann–Hausdorff measure and Holmes–Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH‐minimal surfaces in a Randers domain of constant flag curvature , which are the first examples of BH‐minimal surfaces in the hyperbolic Randers space. 相似文献
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We study the topology of (properly) immersed complete minimal surfaces P 2 in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces (see [10]). We present an alternative and unified proof of the Chern-Osserman inequality satisfied by these minimal surfaces (in ? n and in ? n (b)), based in the isoperimetric analysis mentioned above. Finally, we show a Chern-Osserman-type equality attained by complete minimal surfaces in the Hyperbolic space with finite total extrinsic curvature. 相似文献
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D. V. Bolotov 《Mathematical Notes》2007,82(1-2):10-12
We prove that the hyperbolic space L n cannot be immersed in an Euclidean space E n+m with a flat normal connection provided the module of the mean curvature vector is bounded. 相似文献
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Johan Deprez 《Journal of Geometry》1985,25(2):192-200
Semi-parallel immersions are defined as extrinsic analogue for semi-symmetric spaces and as a direct generalization of parallel immersions. Using results of Backes on Euclidean Jordan triple systems, the totally geodesic immersions are shown to be the only minimal semi-parallel immersions into a Euclidean space. Semi-parallel immersions of surfaces into Em are studied and a classification of semi-parallel immersions with pointwise planar normal sections of surfaces in Em is given.Research Assistant of the National Fund of Scientific Research 相似文献
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Conformally flat submanifolds of Euclidean space 总被引:3,自引:0,他引:3
John Douglas Moore 《Mathematische Annalen》1977,225(1):89-97
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Urs Lang 《Mathematische Zeitschrift》1992,210(1):581-592
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Rafael López 《Calculus of Variations and Partial Differential Equations》2010,39(3-4):333-359
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature H at each point x satisfies 2H(x) = a r(x)2 + b, where r(x) denotes the distance from x to a fixed straight-line L, and a and b are constants. These surfaces are solutions of a variational problem that describes the shape of a drop of incompressible fluid in equilibrium by the action of surface tension when it rotates about L with constant angular velocity. The effect of gravity is neglected. In this paper we study the geometric configurations of such surfaces, focusing the relationship between the geometry of the surface and the one of its boundary. As special cases, we will consider two families of such surfaces: axisymmetric surfaces and embedded surfaces with planar boundary. 相似文献
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