Results 11 to 20 of about 577,330 (363)
The Existence of a Weak Solution to Volume Preserving Mean Curvature Flow in Higher Dimensions [PDF]
Archive for Rational Mechanics and Analysis, 2022 In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of $$L^2$$ L 2 -flow.
K. Takasao
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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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Noncompact self-shrinkers for mean curvature flow with arbitrary genus [PDF]
Journal für die Reine und Angewandte Mathematik, 2021 In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigorous existence proof for these surfaces.
R. Buzano, H. Nguyen, Mario B. Schulz
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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 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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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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Gaussian mean curvature flow [PDF]
Journal of Evolution Equations, 2010 10 ...
Borisenko, Alexander A., Miquel, Vicente
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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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