Results 1 to 10 of about 474 (43)
Geometry of CMC surfaces of finite index
Advanced Nonlinear Studies, 2023 Given r0>0{r}_{0}\gt 0, I∈N∪{0}I\in {\mathbb{N}}\cup \left\{0\right\}, and K0,H0≥0{K}_{0},{H}_{0}\ge 0, let XX be a complete Riemannian 3-manifold with injectivity radius Inj(X)≥r0\hspace{0.1em}\text{Inj}\hspace{0.1em}\left(X)\ge {r}_{0} and with the ...
Meeks William H., Pérez Joaquín
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Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group
Complex Manifolds, 2022 We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method.
Dorfmeister Josef F. +2 more
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Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 In Lorentz-Minkowski 3-space, null scrolls are ruled surfaces with a null base curve and null rulings. Their mean, as well as their Gaussian curvature, depends only on a parameter of a base curve. In the present paper, we obtain the first-order nonlinear
Šipuš Željka Milin +2 more
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Sym-Bobenko formula for minimal surfaces in Heisenberg space [PDF]
, 2013 We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces ...
Cartier, Sébastien
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 In this paper, we construct a helicoidal surface of type I+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3−space ℝ13${\Bbb R}_1^3$with a positive density function. We get a result for minimal case.
Yıldız Önder Gökmen +2 more
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An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C) [PDF]
, 2003 For null curves in PSL(2,C), there exists a representation formula in terms of two meromorphic functions and their derivatives (Small's formula). In this paper, we give an elementary proof of Small's formula.
Kokubu, Masatoshi +2 more
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Survey on real forms of the complex A2(2)-Toda equation and surface theory
Complex Manifolds, 2019 The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop ...
Dorfmeister Josef F. +3 more
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The number of conformally equivalent maximal graphs [PDF]
, 2010 We show that the number of entire maximal graphs with finitely many singular points that are conformally equivalent is a universal constant that depends only on the number of singularities, namely 2n for graphs with n + 1 singularities.
Fernández Delgado, Isabel
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Ramification estimates for the hyperbolic Gauss map [PDF]
, 2008 We give the best possible upper bound on the number of exceptional values and the totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic constant mean curvature one surfaces in the hyperbolic three-space and some partial results ...
Kawakami, Yu
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Parallel Mean Curvature Surfaces in Symmetric Spaces
, 2011 We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric ...
H. Alencar +4 more
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