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Signal Processing, 2019 In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient ...
Goksel, Orcun, Gong, Yuanhao
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Constant mean curvature surfaces [PDF]
Surveys in Differential Geometry, 2016 In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n ...
Meeks III, William H. +2 more
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The mean curvature at the first singular time of the mean curvature flow [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that the
Brakke +26 more
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Curvature estimates for surfaces with bounded mean curvature [PDF]
Transactions of the American Mathematical Society, 2011 Estimates for the norm of the second fundamental form, $|A|$, play a crucial role in studying the geometry of surfaces. In fact, when $|A|$ is bounded the surface cannot bend too sharply.
Bourni, Theodora, Tinaglia, Giuseppe
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Mean curvature flow with obstacles [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012 We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme.
Almeida, Luís +2 more
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The hyperbolic mean curvature flow [PDF]
Journal de Mathématiques Pures et Appliquées, 2007 We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector.
LeFloch, Philippe G., Smoczyk, Knut
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Spacelike Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2018 AbstractWe prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space$$\mathbb {R}^{n,m}$$Rn,m, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove long-time existence and convergence of the$${{\,\mathrm{G}\
Ben Lambert, Jason D. Lotay
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Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2018 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
M. Gromov
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Mean curvature and texture constrained composite weighted random walk algorithm for optic disc segmentation towards glaucoma screening [PDF]
Healthcare Technology Letters, 2018 Accurate optic disc (OD) segmentation is an important step in obtaining cup-to-disc ratio-based glaucoma screening using fundus imaging. It is a challenging task because of the subtle OD boundary, blood vessel occlusion and intensity inhomogeneity.
Rashmi Panda, N.B. Puhan, Ganapati Panda
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Surfaces of constant mean curvature [PDF]
Proceedings of the American Mathematical Society, 1966 Joseph A. Wolf
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