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Motion of level sets by mean curvature
 II, Trans. Amer. Math. Soc
"... We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γ o a unique generalized motion by mean curvature, existing for all time. We investigate the various ..."
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Cited by 435 (6 self)
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We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γ o a unique generalized motion by mean curvature, existing for all time. We investigate the various
MEAN CURVATURE BLOWUP IN MEAN CURVATURE FLOW
, 902
"... Abstract. In this note we establish that finitetime singularities of the mean curvature flow of compact Riemannian submanifolds Mm t ֒ → (Nm+n, h) are characterised by the blow up of the mean curvature. 1. ..."
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Cited by 3 (0 self)
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Abstract. In this note we establish that finitetime singularities of the mean curvature flow of compact Riemannian submanifolds Mm t ֒ → (Nm+n, h) are characterised by the blow up of the mean curvature. 1.
• Mean Curvature Flow
, 2005
"... Computation of geometric partial differential equations and mean curvature flow ..."
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Computation of geometric partial differential equations and mean curvature flow
Algorithms for computing motion by mean curvature
 SIAM J. Numer. Anal
, 1996
"... Algorithms for computing motion by mean curvature ..."
MEAN CURVATURE IN MINKOWSKI SPACES
"... Mean curvature of submanifolds in the Euclidean Space is a well established concept, an old and active research field. When we face to the same concept in a finite dimensional normed space, we have many choices for the definition of mean curvature of a submanifold. Here we shall concentrate on norme ..."
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Mean curvature of submanifolds in the Euclidean Space is a well established concept, an old and active research field. When we face to the same concept in a finite dimensional normed space, we have many choices for the definition of mean curvature of a submanifold. Here we shall concentrate
SURFACES WITH PARALLEL MEAN CURVATURE
, 807
"... Abstract. Two holomorphic Hopf differentials for surfaces of nonnull parallel mean curvature vector in S 2 ×S 2 and H 2 ×H 2 are constructed. A 1:1 correspondence between these surfaces and pairs of constant mean curvature surfaces of S 2 × R and H 2 × R is established. Using that, surfaces with va ..."
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Cited by 4 (1 self)
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Abstract. Two holomorphic Hopf differentials for surfaces of nonnull parallel mean curvature vector in S 2 ×S 2 and H 2 ×H 2 are constructed. A 1:1 correspondence between these surfaces and pairs of constant mean curvature surfaces of S 2 × R and H 2 × R is established. Using that, surfaces
ON THE EXTENSION OF THE MEAN CURVATURE FLOW
, 905
"... Abstract. Consider a family of smooth immersions F(·, t) : Mn → Rn+1 of closed hypersurfaces in Rn+1 moving by the mean curvature flow ∂F(p,t) ∂t = −H(p, t) · ν(p, t), for t ∈ [0, T). In [3] Cooper has recently proved that the mean curvature blows up at the singular time T. We show that if the seco ..."
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Cited by 8 (2 self)
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Abstract. Consider a family of smooth immersions F(·, t) : Mn → Rn+1 of closed hypersurfaces in Rn+1 moving by the mean curvature flow ∂F(p,t) ∂t = −H(p, t) · ν(p, t), for t ∈ [0, T). In [3] Cooper has recently proved that the mean curvature blows up at the singular time T. We show
The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality
 J. DIFFERENTIAL GEOM
, 1998
"... In this paper we develop the theory of weak solutions for the inverse mean curvature flow of hypersurfaces in a Riemannian manifold, and apply it to prove the Riemannian version of the Penrose inequality for the total mass of an asymptotically flat 3manifold of nonnegative scalar curvature, announc ..."
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Cited by 201 (0 self)
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In this paper we develop the theory of weak solutions for the inverse mean curvature flow of hypersurfaces in a Riemannian manifold, and apply it to prove the Riemannian version of the Penrose inequality for the total mass of an asymptotically flat 3manifold of nonnegative scalar curvature
Prescribing Mean Curvature Vectors for Foliations
, 2002
"... Prescribing mean curvature vectors for foliations \Lambda ..."
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Cited by 3 (0 self)
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Prescribing mean curvature vectors for foliations \Lambda
Results 1  10
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