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	A variational problem for submanifolds in a sphere
	Guo, Zhen ; Li, Haizhong
	2010-05-06 ; 2010-05-06
关键词	Euler-Lagrangian equation integral inequality Clifford torus Veronese surface WILLMORE SURFACES S-N RIGIDITY THEOREMS COMPACT SURFACES HYPERSURFACES CURVATURE Mathematics
中文摘要	Let x: M -> Sn+p be an n-dimensional submanifold in an (n + p)-dimensional unit sphere Sn+p, M is called a Willmore submanifold (see [11], [16]) if it is a critical submanifold to the Willmore functional integral(M)(S - nH)(n/2)dv, where S = Sigma(alpha,i,j)(h(ij)(alpha))(2) is the square of the length of the second fundamental form, H is the mean curvature of M. In [11], the second author proved an integral inequality of Simons' type for n-dimensional compact Willmore submanifolds in Sn+p. In this paper, we discover that a similar integral inequality of Simons' type still holds for the critical submanifolds of the functional integral(M) (S - nH(2))dv. Moreover, it has the advantage that the corresponding Euler-Lagrange equation is simpler than the Willmore equation.
语种	英语 ; 英语
出版者	SPRINGER WIEN ; WIEN ; SACHSENPLATZ 4-6, PO BOX 89, A-1201 WIEN, AUSTRIA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13875]
专题	清华大学
推荐引用方式 GB/T 7714	Guo, Zhen,Li, Haizhong. A variational problem for submanifolds in a sphere[J],2010, 2010.
APA	Guo, Zhen,&Li, Haizhong.(2010).A variational problem for submanifolds in a sphere..
MLA	Guo, Zhen,et al."A variational problem for submanifolds in a sphere".(2010).

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