منابع مشابه
Some Remarks Concerning Integrals of Curvature on Curves and Surfaces
In this paper we discuss some topics that came up in Chapters 2 and 3 of Part III of [8]. These involve relations between derivatives of Cauchy integrals on curves and surfaces and curvatures of the curves and surfaces. In R for n > 2, “Cauchy integrals” can be based on generalizations of complex analysis using quarternions or Clifford algebras (as in [3]). Part of the point here is to bring ou...
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In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; they are classified using their asymptotic necksizes. We work in a class slightl...
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For each embedded constant mean curvature surface in R 3 with three ends and genus zero, we construct a conjugate cousin boundary contour in S 3. The moduli space of such contours is parametrized by the space of triples of distinct points in S 2. This imposes necessary conditions on the cmc surfaces; moreover, we expect the space of triples exactly parametrizes their moduli space. Our approach ...
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In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...
متن کاملComplete surfaces with negative extrinsic curvature
N. V. Efimov [Efi64] proved that there is no complete, smooth surface in R with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if M has sectional curvature between two constants K2 and K3, then there exists K1 < min(K2, 0) such that M contains no smooth, complete immersed surface with curvature below K1. Optimal values of K1 are dete...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/154294