Results 1 to 10 of about 134 (57)
Advanced Nonlinear StudiesWe describe new annular examples of complete translating solitons for the mean curvature flow and how they are related to a family of translating graphs, the Δ-wings.
Hoffman David +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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The evolution of immersed locally convex plane curves driven by anisotropic curvature flow
Advances in Nonlinear Analysis, 2022 In this article, we study the evolution of immersed locally convex plane curves driven by anisotropic flow with inner normal velocity V=1αψ(x)καV=\frac{1}{\alpha }\psi \left(x){\kappa }^{\alpha } for α1\alpha \gt 1, where x∈[0,2mπ]x\in \left[0,2m\pi ] is
Wang Yaping, Wang Xiaoliu
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Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies [PDF]
, 2020 We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based
Fischer, Julian +2 more
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Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces
Advanced Nonlinear Studies, 2023 We survey some ideas regarding the application of the Aleksandrov reflection method in partial differential equation to extrinsic geometric flows of Euclidean hypersurfaces.
Chow Bennett
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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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On obstacle problem for Brakke's mean curvature flow [PDF]
, 2021 We consider the obstacle problem of the weak solution for the mean curvature flow, in the sense of Brakke's mean curvature flow. We prove the global existence of the weak solution with obstacles which have $C^{1,1}$ boundaries, in two and three space ...
Takasao, Keisuke
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An unconditionally stable finite element scheme for anisotropic curve shortening flow [PDF]
, 2023 summary:Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler
Deckelnick, Klaus, Nürnberg, Robert
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, 2023 In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are translating solitons for the inverse mean curvature flow.
Neto, Gregório Silva, Silva, Vanessa
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The structure of translating surfaces with finite total curvature [PDF]
, 2023 In this paper, we prove that any mean curvature flow translator Σ2 ⊂ R3 with finite total curvature and one end must be a plane. We also prove that if the translator Σ has multiple ends, they are asymptotic to a plane Π containing the direction of ...
Khan, Ilyas
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