Ni, Flow by the power of the Gauss curvature. In preparation.Andrews, B; Guan, P. F.; Ni, L.: Flow by power of the Gauss curvature. Adv. Math 299 (2016), 174-201.Andrews, B., Guan, P., and Ni, L. Flow by the power of the gauss curvature. arXiv preprint arXiv:1510.00655...
We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the m-th mean curvature plus a volume preserving term, including the case of powers of the mean curvature or of the Gauss
Gauss curvature flow: the fate of the rolling stones 来自 掌桥科研 喜欢 0 阅读量: 112 作者: B Andrews 摘要: We prove Firey's 1974 conjecture that convex surfaces moving by their Gauss curvature become spherical as they contract to points. 关键词: Mathematics Subject Classification (1991):...
Evolution of convex hypersurfaces by powers of the mean curvature We study the evolution of a closed, convex hypersurface in n +1 in direction of its normal vector, where the speed equals a positive power k of the me... F Schulze - 《Mathematische Zeitschrift》 被引量: 157发表: 2005年 ...
in powers of \({\bar{u}}\) . a first approach is a naive perturbation series ansatz $$\begin{aligned} {\bar{c}}_n(\rho ) = \sum _{m=0}^\infty {\bar{u}}^m {\bar{c}}_n^{(m)}(\rho ) \end{aligned}$$ (27) for each legendre coefficient starting with \({\bar{c}}...
continue to be shed in the upper section of the cylinder (). As the cylinder begins to rotate, a large-scale motion becomes apparent on the high-pressure side, close to the bottom wall. We offer both a qualitative and quantitative description of this motion, outlining its impact on the ...
Negative powers We classify all complete noncompact embedded convex hypersurfaces in $mathbf{R}^{n+1}$ which move homothetically under flow by some negative power of their Gauss curvature. J Urbas - 《Advances in Differential Equations》
Flow by powers of the Gauss curvature in space formsMin ChenJiuzhou Huang
CURVATUREWe consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior....
We give a simple proof of an extension of the existence results of Ricci flow of G.Giesen and P.M.Topping [GiT1],[GiT2], on incomplete surfaces with bounded above Gauss curvature without using the difficult Shi's existence theorem of Ricci flow on complete non-compact surfaces and the ...