Results 21 to 30 of about 255,201 (317)
Gaussian mean curvature flow [PDF]
Journal of Evolution Equations, 2010 10 ...
A. A. Borisenko, Vicente Miquel
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Spacelike Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2019 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 flow with surgery [PDF]
Duke Mathematical Journal, 2017 We give a new proof for the existence of mean curvature flow with surgery of 2-convex hypersurfaces in $R^N$, as announced in arXiv:1304.0926. Our proof works for all $N \geq 3$, including mean convex surfaces in $R^3$. We also derive a priori estimates for a more general class of flows in a local and flexible setting.
Haslhofer, Robert, Kleiner, Bruce
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Bulletin of the American Mathematical Society, 2015 Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then
Colding, Tobias +2 more
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On mean curvature flow with forcing [PDF]
Communications in Partial Differential Equations, 2019 This paper investigates geometric properties and well-posedness of a mean curvature flow with volume-dependent forcing. With the class of forcing which bounds the volume of the evolving set away from zero and infinity, we show that a strong version of star-shapedness is preserved over time.
Inwon Kim, Dohyun Kwon
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Mean curvature flow with obstacles
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. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the ...
Almeida, Luís +2 more
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Hamiltonian mean curvature flow [PDF]
International Journal of Contemporary Mathematical Sciences, 2013 Let ( , ) be a compact Riemann surface with constant curvature c. In this work, we proved that the mean curvature flow of a given Hamiltonian diffeomorphism on provides a smooth path in Ham( ), the group of all Hamiltonian diffeomorphisms of .
Leonard Todjihounde, Djideme F. Houenou
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Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation
Mathematics, 2021 The Poisson surface reconstruction algorithm has become a very popular tool of reconstruction from point clouds. If we reconstruct each region separately in the process of multi-reconstruction, then the reconstructed objects may overlap with each other ...
Jin Wang, Zhengyuan Shi
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Self-Expanders of the Mean Curvature Flow [PDF]
Vietnam Journal of Mathematics, 2021 AbstractWe study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ
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Communications in Contemporary Mathematics, 2019 The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of a short-time solution to the initial value problem of the SMCF of compact surfaces in Euclidean space [Formula ...
Chong Song, Jun Sun
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