Results 31 to 40 of about 577,330 (363)
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions [PDF]
Journal of the European Mathematical Society (Print), 2020 We prove that in the absence of topological changes, the notion of \operatorname{BV} solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness.
J. Fischer +3 more
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Hyperbolic mean curvature flow
Journal of Differential Equations, 2009 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 short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive
He, Chun-Lei, Kong, De-Xing, Liu, Kefeng
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Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow [PDF]
Analysis & PDE, 2020 We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in R^{n+1} is close to a constant in L^{n}-sense, then the set is close to a union of disjoint balls with respect to the Hausdorff ...
Vesa Julin, J. Niinikoski
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Mean Curvature Flow of Mean Convex Hypersurfaces [PDF]
Communications on Pure and Applied Mathematics, 2016 In the last 15 years, White and Huisken‐Sinestrari developed a far‐reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high‐curvature regions in a mean convex flow.In the present paper, we give a ...
Haslhofer, Robert, Kleiner, Bruce
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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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Universality in mean curvature flow neckpinches [PDF]
, 2014 We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically
Gang, Zhou, Knopf, Dan
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Mean curvature flow and Riemannian submersions [PDF]
, 2015 We give a sufficient condition ensuring that the mean curvature flow commutes with a Riemannian submersion and we use this result to create new examples of evolution by mean curvature flow.
Pipoli, Giuseppe
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Mean-Curvature Flow of Voronoi Diagrams [PDF]
Journal of Nonlinear Science, 2014 We study the evolution of grain boundary networks by the mean-curvature flow under the restriction that the networks are Voronoi diagrams for a set of points. For such evolution we prove a rigorous universal upper bound on the coarsening rate. The rate agrees with the rate predicted for the evolution by mean-curvature flow of the general grain boundary
Elsey, Matt, Slepčev, Dejan
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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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Formal asymptotic expansions for symmetric ancient ovalsin mean curvature flow
Networks and Heterogeneous Media, 2013 We provide formal matched asymptotic expansions for ancient convex solutions to MCF. The formal analysis leading to the solutions is analogous to that for the generic MCF neck pinch in [1].
Sigurd Angenent
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