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A remark on soliton equation of mean curvature flow [PDF]

Anais da Academia Brasileira de Ciências, 2004
In this note, we consider self-similar immersions of the mean curvature flow and show that a graph solution of the soliton equation, provided it has bounded derivative, converges smoothly to a function which has some special properties (see Theorem 1.1 ...
Li Ma, Yang Yang
doaj   +2 more sources

Self-Expanders of the Mean Curvature Flow [PDF]

Vietnam Journal of Mathematics, 2020
AbstractWe study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ
Knut Smoczyk
semanticscholar   +4 more sources

Width and mean curvature flow [PDF]

Geometry & Topology, 2007
Given a Riemannian metric on a homotopy $n$-sphere, sweep it out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as possible yet preserving the sweepout.
Tobias Colding, William P. Minicozzi
openalex   +6 more sources

The hyperbolic mean curvature flow

Journal de Mathématiques Pures et Appliquées, 2007
26 ...
Philippe G. LeFloch, Knut Smoczyk
openalex   +5 more sources

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

The Extension for Mean Curvature Flow with Finite Integral Curvature in Riemannian Manifolds [PDF]

arXiv, 2009
We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature on a finite time interval $[0,T)$ can be extended over time $T$. Moreover, we show that the condition is optimal in some sense.
Hongwei Xu, Fei Ye, Entao Zhao
arxiv   +3 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
doaj   +2 more sources

Mean curvature blow up in mean curvature flow

, 2009
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds are characterised by the blow up of the mean curvature.
Andrew A. Cooper
openalex   +4 more sources

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source