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A remark on soliton equation of mean curvature flow [PDF]
Anais da Academia Brasileira de Ciências, 2004 In this note, we consider self-similar immersions of the mean curvature flow and show that a graph solution of the soliton equation, provided it has bounded derivative, converges smoothly to a function which has some special properties (see Theorem 1.1 ...
Li Ma, Yang Yang
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The fractional mean curvature flow
Bruno Pini Mathematical Analysis Seminar, 2020 In this note, we present some recent results in the study of the fractional mean curvature flow, that is a geometric evolution of the boundary of a set whose speed is given by the fractional mean curvature.
Eleonora Cinti
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Pinched hypersurfaces are compact
Advanced Nonlinear Studies, 2023 We make rigorous and old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.
Bourni Theodora +2 more
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Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products
Analysis and Geometry in Metric Spaces, 2022 Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞.
Casteras Jean-Baptiste +3 more
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Nonlocal diffusion of smooth sets
Mathematics in Engineering, 2022 We consider normal velocity of smooth sets evolving by the $ s- $fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $ s\in [\frac{1}{2},
Anoumou Attiogbe +2 more
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Recent rigidity results for graphs with prescribed mean curvature
Mathematics in Engineering, 2021 This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → R. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow ...
Bruno Bianchini +5 more
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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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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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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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