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Recent rigidity results for graphs with prescribed mean curvature
Mathematics in Engineering, 2021 This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → R. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow ...
Bruno Bianchini +5 more
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Existence of hypersurfaces with prescribed mean curvature I – generic min-max [PDF]
Cambridge Journal of Mathematics, 2018 We prove that, for a generic set of smooth prescription functions $h$ on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean curvature $h$.
Xin Zhou, Jonathan J. Zhu
semanticscholar +1 more source
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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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
core +3 more sources
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
core +2 more sources
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
semanticscholar +1 more source
Hyperbolic mean curvature flow
Journal of Differential Equations, 2009 In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive
He, Chun-Lei, Kong, De-Xing, Liu, Kefeng
openaire +2 more sources
Bulletin of the American Mathematical Society, 2015 Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then
Colding, Tobias +2 more
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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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Preconditioned augmented Lagrangian method for mean curvature image deblurring
AIMS Mathematics, 2022 Image deblurring models with a mean curvature functional has been widely used to preserve edges and remove the staircase effect in the resulting images. However, the Euler-Lagrange equations of a mean curvature model can be used to solve fourth-order non-
Shahbaz Ahmad +6 more
doaj +1 more source