Results 1 to 10 of about 31 (31)
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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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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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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α-Mean curvature flow of non-compact complete convex hypersurfaces and the evolution of level sets
Advances in Nonlinear AnalysisWe consider the α\alpha -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are ...
Kang Hyunsuk, Lee Ki-Ahm, Lee Taehun
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Lower bounds on density for topologically nontrivial minimal cones up to dimension six
Forum of Mathematics, SigmaWe prove lower bounds on the density of regular minimal cones of dimension less than seven provided the complements of the cones are topologically nontrivial.
Jacob Bernstein, Lu Wang
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Conservation laws that depend on functions and PDE reduction: Extending Noether $1\tfrac {1}{2}$
European Journal of Applied MathematicsThis paper develops methods for simplifying systems of partial differential equations (PDEs) that have families of conservation laws which depend on arbitrary functions of the independent or dependent variables. Cases are identified in which such methods
Peter E. Hydon, John R. King
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Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow
European Journal of Applied MathematicsThe purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative ...
Tim Laux +2 more
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Advances in Nonlinear AnalysisOur purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions ...
Batista Márcio +3 more
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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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