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991.
In this note, we will prove a Kähler version of Cheeger-Gromoll-Perelman's soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point. 相似文献
992.
研究球面S~4到CP~n的常曲率弱Lagrangian极小浸入■:S~4→CP~n.如果■的诱导度量ds~2具有常(截面)曲率c,则存在一个整数s≥1,使得c=4/[s(s+3)].浸入■被两个四元齐次多项式f_s和f_(s-1)唯一确定.当s=1,即c=1,或s=2,即c=2/5时,浸入■是绝对实的. 相似文献
993.
Ke Chen 《Numerical Methods for Partial Differential Equations》2012,28(6):1966-1995
In a multimodal image registration scenario, where two given images have similar features, but noncomparable intensity variations, the sum of squared differences is not suitable for inferring image similarities. In this article, we first propose a new variational model based on combining intensity and geometric transformations, as an alternative to use mutual information and an improvement to the work by Modersitzki and Wirtz (Modersitzki and Wirtz, Lect Notes Comput Sci 4057 (2006), 257–263), and then develop a fast multigrid (MG) algorithm for solving the underlying system of fourth‐order and nonlinear partial differential equations. We can demonstrate the effective smoothing property of the adopted primal‐dual smoother by a local Fourier analysis. Numerical tests will be presented to show both the improvements achieved in image registration quality and MG efficiency. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
994.
995.
华义平 《纯粹数学与应用数学》2012,28(3):308-312
M是一个紧致的局部共形平坦黎曼流形,其上定义的Schouten张量是一个Codazzi张量.本文借助这个Codazzi张量引入Cheng和Yau的自伴算子,从而获得了局部共形平坦流形上的一些性质,改进了已有的结论. 相似文献
996.
A smooth, compact and strictly convex hypersurface evolving in ℝ
n+1 along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We
show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink
to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough.
The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper.
Long-time existence and convergence of normalization of the flow are also investigated. 相似文献
997.
In this paper, we obtain a constraint of the mean curvature for proper biharmonic submanifolds in a sphere. We give some characterizations
of some proper biharmonic submanifolds with parallel mean curvature vector in a sphere. We also construct some new examples
of proper biharmonic submanifolds in a sphere. 相似文献
998.
In this paper we prove an ε0-regularity theorem for mean curvature flow from surface to a flat Riemannian manifold. More precisely, we prove that if the initial energy ∫Σ0 |A|2 ≤ε0 and the initial area μ0(Σ0) is not large, then along the mean curvature flow, we have ∫Σt|A|2 ≤ε0. As an application, we obtain the long time existence and convergence result of the mean curvature flow. 相似文献
999.
In this paper,we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional M2p of a submanifold M n in a general Riemannian manifold N n+m for p = 0,1,...,[n 2 ].As an example,we prove that closed complex submanifolds in complex projective spaces are critical points of the functional M2p,called relatively 2p-minimal submanifolds,for all p.At last,we discuss the relations between relatively 2p-minimal submanifolds and austere submanifolds in real space forms,as well as a special variational problem. 相似文献
1000.
Yi Li 《中国科学 数学(英文版)》2012,55(1):99-118
In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting. 相似文献