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110,077
• 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
Hyperbolic Mean Curvature Flow
"... 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 shorttime smooth solution and possesses the nonlinear stability defined on the ..."
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Cited by 3 (2 self)
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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 shorttime smooth solution and possesses the nonlinear stability defined
Riemannian Mean Curvature Flow
"... Abstract. In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution p ..."
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Abstract. In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution
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 7 (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
MEAN CURVATURE FLOW WITHOUT SINGULARITIES
, 2012
"... Abstract. We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying gr ..."
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Cited by 1 (0 self)
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Abstract. We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying
MEAN CURVATURE FLOW WITHOUT SINGULARITIES
"... Abstract. We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying gr ..."
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Abstract. We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying
SINGULAR PERTURBATIONS OF MEAN CURVATURE FLOW
, 2004
"... Abstract. We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity. ..."
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Cited by 5 (3 self)
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Abstract. We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.
BACKWARDS UNIQUENESS OF THE MEAN CURVATURE FLOW
, 907
"... Abstract. In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let Ft, e Ft: M n → M n+1 be two complete solutions of the mean curvature flow on M n ×[0, T] with bounded second fundamental form in a complete ambient manifold with bounded g ..."
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Abstract. In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let Ft, e Ft: M n → M n+1 be two complete solutions of the mean curvature flow on M n ×[0, T] with bounded second fundamental form in a complete ambient manifold with bounded
Singularity profile in the mean curvature flow
, 2009
"... In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space R n+1 with positive mean curvature is κnoncollapsing, and a blowup ..."
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Cited by 14 (2 self)
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In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space R n+1 with positive mean curvature is κnoncollapsing, and a blow
MEAN CURVATURE FLOW AND LAGRANGIAN EMBEDDINGS
"... In this note we provide examples of compact embedded lagrangians in C n for any n ≥ 2 that under mean curvature flow develop singularities in finite time. When n is odd the lagrangians can be taken to be orientable. By gluing these lagrangians onto a special lagrangian embedding L we provide ..."
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Cited by 2 (0 self)
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In this note we provide examples of compact embedded lagrangians in C n for any n ≥ 2 that under mean curvature flow develop singularities in finite time. When n is odd the lagrangians can be taken to be orientable. By gluing these lagrangians onto a special lagrangian embedding L we provide
Results 1  10
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