Results 11 to 20 of about 1,076 (51)
The double bubble problem in spherical and hyperbolic space
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 11, Page 641-699, 2002., 2002 We prove that the standard double bubble is the least‐area way to enclose and separate two regions of equal volume in ℍ3, and in S3 when the exterior is at least ten percent of S3.
Andrew Cotton, David Freeman
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On the new approach for the energy of elastica
Acta Scientiarum: Technology, 2018 In this work, we firstly describe conditions for being elastica in Minkowski space E41. Then we investigate the energy of the elastic curves and exploit its relationship with the energy of Bishop vectors belong to that elastic curves E41.
Talat Körpınar, Rıdvan Cem Demirkol
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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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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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A boundary value problem in the hyperbolic space
Abstract and Applied Analysis, Volume 4, Issue 4, Page 249-253, 1999., 1999 We consider a nonlinear problem for the mean curvature equation in the hyperbolic space with a Dirichlet boundary data g. We find solutions in a Sobolev space under appropriate conditions on g.
P. Amster, G. Keilhauer, M. C. Mariani
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Bifurcation of the equivariant minimal interfaces in a hydromechanics problem
Abstract and Applied Analysis, Volume 1, Issue 3, Page 291-304, 1996., 1996 In this work we study a deformation of the minimal interface of two fluids in a vertical tube under the presence of gravitation. We show that a symmetry of the base of tube let us to apply a method developed earlier by the first author and based on the Crandall‐Rabinowitz bifurcation theorem.
A. Y. Borisovich, W. Marzantowicz
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Hyperbolic Unfoldings of Minimal Hypersurfaces
Analysis and Geometry in Metric Spaces, 2018 We study the intrinsic geometry of area minimizing hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. Namely, for any such hypersurface H we define and construct a so-called S-structure.
Lohkamp Joachim
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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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On the umbilic set of immersed surfaces in three-dimensional space forms
, 2019 We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated
Catino, Giovanni +2 more
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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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