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Notes on Translating Solitons for Mean Curvature Flow [PDF]
Minimal Surfaces: Integrable Systems and Visualisation, 2019 The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$.
D. Hoffman +3 more
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Lietuvos Matematikos Rinkinys, 2010 In this article we generalize some classical formulas for curvatures of hypersurfaces in the n-dimensional Euclidean space using the homogeneous formulas.
Kazimieras Navickis
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Stability of helicoidal surfaces with constant mean curvature
International Journal of Mathematics for Industry, 2020 Motivated by an experimental result on the shape of liquid water supported by a small stainless helical wire, we find a class of stable helicoidal convex surfaces with constant mean curvature whose boundary consists of a single helix and two short arcs.
Yuta Hatakeyama, Miyuki Koiso
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Mean curvature flow and Riemannian submersions [PDF]
, 2015 We give a sufficient condition ensuring that the mean curvature flow commutes with a Riemannian submersion and we use this result to create new examples of evolution by mean curvature flow.
Pipoli, Giuseppe
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Overdetermined problems and constant mean curvature surfaces in cones [PDF]
Revista matemática iberoamericana, 2018 We consider a partially overdetermined problem in a sector-like domain $\Omega$ in a cone $\Sigma$ in $\mathbb{R}^N$, $N\geq 2$, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that $\Omega$ is a spherical ...
F. Pacella, G. Tralli
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On Total Shear Curvature of Surfaces in E^{n+2}
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018 In the present study we consider surfaces in Euclidean (n+2)-space Eⁿ⁺². Firstly, we introduce some basic concepts of second fundamental form and curvatures of the surfaces in Eⁿ⁺².
Kadri Arslan, Betül Bulca
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Maslov, Chern-Weil and Mean Curvature [PDF]
, 2018 We provide an integral formula for the Maslov index of a pair $(E,F)$ over a surface $\Sigma$, where $E\rightarrow\Sigma$ is a complex vector bundle and $F\subset E_{|\partial\Sigma}$ is a totally real subbundle.
Pacini, Tommaso
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Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces [PDF]
Journal of differential geometry, 2018 In this paper we prove that the generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one.
Ao Sun
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Examples of surfaces of constant mean curvature
Дифференциальная геометрия многообразий фигур, 2019 A surface in E3 is called parallel to the surface M if it consists of the ends of constant length segments, laid on the normals to the surfaces at points of this surface. The tangent planes at the corresponding points will be parallel.
M. A. Cheshkova
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Circulant preconditioners for mean curvature-based image deblurring problem
Journal of Algorithms & Computational Technology, 2021 The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the ...
Shahbaz Ahmad, Faisal Fairag
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