منابع مشابه
Ruled Laguerre minimal surfaces
A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...
متن کاملLaguerre Minimal Surfaces
Laguerreminimal (L-minimal) surfaces are theminimizers of the energy ∫ (H2 −K)/KdA. They are a Laguerre geometric counterpart of Willmore surfaces, the minimizers of ∫ (H2 − K)dA, which are known to be an entity of Möbius sphere geometry. The present paper provides a new and simple approach to L-minimal surfaces by showing that they appear as graphs of biharmonic functions in the isotropic mode...
متن کاملBiharmonic Maps and Laguerre Minimal Surfaces
and Applied Analysis 3 2.5. Laguerre Surface. LetΦ be a Laguerre surface inR. Any regular pointP onΦ is thus represented as in (16). Denote the corresponding isotropic surface by Φ with P given by (16). By duality, their corresponding curvatures are related by H ∗ = H K , K ∗ = 1 K . (17) Blaschke [6] defined the middle tangent sphere to be the tangent to the tangent plane P with radius
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We describe a circle-sum construction of smoothly embedded surface in a smooth 4-manifold. We apply this construction to give a simpler solution of the minimal genus problem for nontrivial S2 bundles over surfaces. We also treat the case of blow-ups.
متن کاملRuled minimal surfaces in R with density e
We classify ruled minimal surfaces in R3 with density ez. It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in R3 with density ez. It is also proved that all translation minimal surfaces are ruled. AMS Subject Classification (2000): Primary 53C25; Secondary 53A10; 49Q05
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2011
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-011-0953-0