Results 21 to 30 of about 868,975 (356)
Weak-strong uniqueness for volume-preserving mean curvature flow [PDF]
Revista matemática iberoamericana, 2022 In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the ...
Tim Laux
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Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces [PDF]
Numerische Mathematik, 2022 An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a ...
C. M. Elliott +2 more
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A constrained mean curvature flow and Alexandrov-Fenchel inequalities [PDF]
, 2022 In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and the global convergence to a spherical cap.
Xinqun Mei, Guofang Wang, Liangjun Weng
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Mean curvature flow with generic low-entropy initial data [PDF]
Duke mathematical journal, 2021 We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem applies to all closed surfaces in $\mathbb{R}^3$ with entropy $\leq 2$ and
Otis Chodosh +3 more
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Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements [PDF]
SIAM Journal on Numerical Analysis, 2021 Dziuk's surface finite element method (FEM) for mean curvature flow has had a significant impact on the development of parametric and evolving surface FEMs for surface evolution equations and curva...
Buyang Li
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Uniqueness of entire graphs evolving by mean curvature flow [PDF]
Journal für die Reine und Angewandte Mathematik, 2021 In this paper we study the uniqueness of graphical mean curvature flow with locally Lipschitz initial data. We first prove that rotationally symmetric entire graphs are unique, without any further assumptions.
P. Daskalopoulos, M. Sáez
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Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
Geometry and Topology, 2021 Suppose that Mt, t ∈ (−∞, 0), is a noncompact ancient solution of mean curvature flow in Rn+1 which is strictly convex, uniformly two-convex, and noncollapsed. We consider the rescaled flow M̄τ = e τ 2 M−e−τ .
S. Brendle, Kyeongsu Choi
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Hyperbolic mean curvature flow [PDF]
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
Chun-Lei He, Kefeng Liu, Dexing Kong
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Gaussian mean curvature flow [PDF]
Journal of Evolution Equations, 2010 10 ...
A. A. Borisenko, Vicente Miquel
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Spacelike Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2019 AbstractWe prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space$$\mathbb {R}^{n,m}$$Rn,m, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove long-time existence and convergence of the$${{\,\mathrm{G}\
Ben Lambert, Jason D. Lotay
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