Results 31 to 40 of about 345,318 (329)
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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Spacelike translating solitons of the mean curvature flow in Lorentzian product spaces with density
Mathematics in Engineering, 2023 By applying suitable Liouville-type results, an appropriate parabolicity criterion, and a version of the Omori-Yau's maximum principle for the drift Laplacian, we infer the uniqueness and nonexistence of complete spacelike translating solitons of the ...
Márcio Batista +2 more
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Anisotropic and crystalline mean curvature flow of mean-convex sets [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature.
A. Chambolle, M. Novaga
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Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow
Discrete Dynamics in Nature and Society, 2020 In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to
Zenggui Wang
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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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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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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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A survey on Inverse mean curvature flow in ROSSes
Complex Manifolds, 2017 In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
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