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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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1994
Given a function \(H\in L^ 1 (\mathbb{R}^ n)\) a measurable set \(E\subset \mathbb{R}^ n\) is said to have variational mean curvature \(H\) if \(E\) minimizes the functional \(F_ H (E)= \int| D\chi_ E|+ \int_ E H(x)dx\), where \(\int| D\chi_ E|\) denotes the total variation of the vector measure \(D\chi_ E\), \(\chi_ E=\) characteristic function of the
MASSARI, Umberto, E. GONZALEZ
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Given a function \(H\in L^ 1 (\mathbb{R}^ n)\) a measurable set \(E\subset \mathbb{R}^ n\) is said to have variational mean curvature \(H\) if \(E\) minimizes the functional \(F_ H (E)= \int| D\chi_ E|+ \int_ E H(x)dx\), where \(\int| D\chi_ E|\) denotes the total variation of the vector measure \(D\chi_ E\), \(\chi_ E=\) characteristic function of the
MASSARI, Umberto, E. GONZALEZ
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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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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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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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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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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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