Results 11 to 20 of about 266,343 (229)
Hyperbolic mean curvature flow
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
He, Chun-Lei, Kong, De-Xing, Liu, Kefeng
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Mean Curvature Flow of Mean Convex Hypersurfaces [PDF]
Communications on Pure and Applied Mathematics, 2016 In the last 15 years, White and Huisken‐Sinestrari developed a far‐reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high‐curvature regions in a mean convex flow.In the present paper, we give a ...
Haslhofer, Robert, Kleiner, Bruce
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Is mean curvature flow a gradient flow?
, 2023 It is well-known that the mean curvature flow is a formal gradient flow of the perimeter functional. However, by the work of Michor and Mumford [7,8], the formal Riemannian structure that is compatible with the gradient flow structure induces a degenerate metric on the space of hypersurfaces.
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Existence of mean curvature flow singularities with bounded mean curvature
Duke Mathematical Journal, 2023 44 pages, comments ...
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Uniformly Compressing Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2018 Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks.
Wenhui Shi, Dmitry Vorotnikov
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Mean curvature flow of spacelike graphs [PDF]
Mathematische Zeitschrift, 2010 We prove the mean curvature flow of a spacelike graph in $(Σ_1\times Σ_2, g_1-g_2)$ of a map $f:Σ_1\to Σ_2$ from a closed Riemannian manifold $(Σ_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(Σ_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\leq K_1$, remains a spacelike graph ...
Li, Guanghan, Salavessa, Isabel M. C.
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Inverse Mean Curvature Flow With Singularities
International Mathematics Research Notices, 2022 Abstract This paper concerns the inverse mean curvature flow (IMCF) running from the boundary of a convex body that has no regularity assumption. We study the evolution of singularities by looking at the blow-up tangent cone around each singular point.
Choi, Beomjun, Hung, Pei-Ken
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The volume preserving mean curvature flow. [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 1987 Let \(F: M^ n\to {\mathbb{R}}^{n+1}\) be the immersion of a uniformly convex closed hypersurface in \({\mathbb{R}}^{n+1}\). \(M^ n\) is deformed by the evolution equation \(\partial F/\partial t=(h-H)\cdot \nu\) where \(\nu\) is the outer unit normal to M, H is the mean curvature and h is the average of H.
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Hyperbolic inverse mean curvature flow [PDF]
Czechoslovak Mathematical Journal, 2019 In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$ ($n\geqslant2$) is mean convex and star-shaped.
Mao, Jing, Wu, Chuan-Xi, Zhou, Zhe
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Mean Convex Mean Curvature Flow with Free Boundary [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractIn this paper, we generalize White's regularity and structure theory for mean‐convex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound
Edelen, Nick +3 more
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