Results 11 to 20 of about 868,975 (356)

Self-Expanders of the Mean Curvature Flow [PDF]

Vietnam Journal of Mathematics, 2021
AbstractWe study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ
Knut Smoczyk
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Mean Curvature Flow on Ricci Solitons [PDF]

Journal of Physics A: Mathematical and Theoretical, 2010
We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature ...
Bakas I, Cao H D Zhu X P, Chow B, Efstratios Tsatis, Fateev V A Onofri E, Hamilton R, Huisken G, Kleiner B Lott J, Mantegazza C Magni A Tsatis E, Morgan J Tian G, Ni L, Perelman G, Perelman G, Perelman G, Zamolodchikov A B, Zamolodchikov A B   +15 more
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Mean curvature flow in a Ricci flow background [PDF]

Communications in Mathematical Physics, 2012
Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow.
B. Kleiner, E. Fan, G. Gibbons, G. Huisken, G. Huisken, G. Huisken, J. Lott, J. Simons, J. York, John Lott, K. Ecker, P.T. Ho, R. Hamilton, R. Hamilton, T. Colding   +14 more
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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 $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\Sigma_2,g_2)$ with ...
A.L. Albujer, B. White, C. Gerhardt, C. Gerhardt, G. Huisken, G. Huisken, G. Huisken, G. Li, Guanghan Li, H. Weyl, I.M.C. Salavessa, I.M.C. Salavessa, Isabel M. C. Salavessa, J. Chen, J. Chen, J. Eells, J. Jost, K. Ecker, K. Ecker, K. Smoczyk, M. Aarons, M.-P. Tsui, M.-T. Wang, M.-T. Wang, R. Hamilton, Y. Xin   +25 more
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Existence of mean curvature flow singularities with bounded mean curvature [PDF]

Duke Mathematical Journal, 2023
44 pages, comments ...
M. Stolarski
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On the extension of the mean curvature flow [PDF]

Mathematische Zeitschrift, 2009
Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot (p,t)$, for $t\in [0,T)$. In \cite{Cooper} Cooper has recently proved that the mean curvature blows up at the singular time $T$. We show that if
Nam Q. Le, Nataša Šešum
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Fattening in mean curvature flow

32 pages, 2 figures.
Ilmanen, Tom, White, Brian
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Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]

Royal Society Open Science
We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
doaj   +2 more sources

Effects of pedicle subtraction osteotomy on aortic morphology and hemodynamics in ankylosing spondylitis with kyphosis: a finite element analysis study [PDF]

Scientific Reports
Osteotomy can correct kyphosis, restore the spinal sequence, and restore the healthy appearance of a patient. However, the aorta is stretched during pedicle subtraction osteotomy (PSO), and some surgeons are concerned about aortic injury.
Weiran Hu, Guang Yang, Xinge Shi, Hongqiang Wang, Kai Zhang, Yanzheng Gao   +5 more
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Inverse mean curvature flow and Ricci-pinched three-manifolds [PDF]

Journal für die Reine und Angewandte Mathematik, 2023
Let ( M , g ) (M,g) be a noncompact, connected, complete Riemannian three-manifold with nonnegative Ricci curvature satisfying Ric ≥ ε ⁢ tr ⁡ ( Ric ) ⁢ g \mathrm{Ric}\geq\varepsilon\operatorname{tr}(\mathrm{Ric})g for some ε > 0 \varepsilon>0 .
G. Huisken, T. Koerber
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