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On Brakke’s mean curvature flow
Sugaku Expositions, 2022The article represents an excellent exposition of a fascinating, resurgent field of research, by one of the main researchers in the domain. It starts from the basic physical intuition and motivation, proceeds through essential background material, such as the mean curvature flow, as well as crucial definitions and tools from geometric measure theory ...
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Nucleation and mean curvature flow
Communications in Partial Differential Equations, 1998which is written in terms of the characteristic function of the evolving set. The argument is based on implicit time-discretization, derivation of uniform estimates, and passage to thIn this paper ...
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Computing Curvature, Mean Curvature and Weighted Mean Curvature
2022 IEEE International Conference on Image Processing (ICIP), 2022openaire +1 more source
Stochastic Motion by Mean Curvature
Archive for Rational Mechanics and Analysis, 1998The author establishes the existence of a continuously time-varying random subset \(K(t)\) of Euclidean space such that its boundary, which is a hypersurface, has normal velocity formally equal to the mean curvature plus a random driving force. This random force is modelled by a stochastic flow of diffeomorphisms, and the sets \(K(t)\) are sets of ...
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Interfaces of Prescribed Mean Curvature
1987Several questions of mathematical and physical interest lead to the consideration of an “energy functional” of the following type: $$F[V] = \text{(weighted area of}\, S) + \int_{v}\, H dv,$$ (*) where S is the surface bounding the region V of n-space and H is a given summable function. In the following, we shall be concerned with a problem of
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Motion by mean curvature and nucleation
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997Summary: A model is proposed to represent mean curvature flow (with forcing term), as well as nucleation and other discontinuities in set evolution. A weak formulation in the framework of BV-spaces is written in terms of the characteristic function of the evolving set. This problem has at least one solution.
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Concentrated Curvature for Mean Curvature Estimation
2010We present a mathematical result that allows computing the discrete mean curvature of a polygonal surface from the so-called concentrated curvature generally used for Gaussian curvature estimation. Our result adds important value to concentrated curvature as a geometric and metric tool to study accurately the morphology of a surface.
M. M. Mesmoudi +2 more
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Hypersurfaces of Constant Mean Curvature
1989I want to discuss some aspects of the theory of hypersurfaces of constant mean curvature H. The subject is intimately related to the theory of minimal hypersurfaces which corresponds to the case H = 0. There are, however, some striking differences between the two cases, and this can already be made clear in the simplest situation of surfaces in the ...
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Globally observed trends in mean and extreme river flow attributed to climate change
Science, 2021Lukas Gudmundsson +2 more
exaly
Boundaries of prescribed mean curvature
1993The author refers to the study of the functional \[ {\mathcal J}_ H(X)= | \partial X|(\Omega)+ \int_ \Omega \phi_ X(x) H(x) dx, \] where \(\Omega\) is an open subset of \(\mathbb{R}^ n\) \((n\geq 2)\), \(H\in L'(\Omega)\), \(\phi_ X\) is the characteristic function of the measurable set \(X\subset \mathbb{R}^ n\) and \(|\partial X|(\Omega)\) is the ...
E. Gonzalez, U. Massari, Tamanini, Italo
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