Constant mean curvature spheres in Riemannian manifolds

被引：0

作者：

F. Pacard

X. Xu

机构：

[1] Université Paris 12,Laboratoire d’Analyse et de Mathématiques Appliquées

[2] Institut Universitaire de France,Department of Mathematics

[3] National University of Singapore,undefined

来源：

manuscripta mathematica | 2009年 / 128卷

关键词：

53A10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove the existence of embedded spheres with large constant mean curvature in any compact Riemannian manifold (M, g). This result partially generalizes a result of R. Ye which handles the case where the scalar curvature function of the ambient manifold (M, g) has non-degenerate critical points.

引用

页码：275 / 295

页数：20

共 9 条

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[2] Meyer D.(2002)Sharp local isoperimetric inequalities involving the scalar curvature Proc. Am. Math. Soc. 130 2351-2361
[3] Druet O.(1991)Compact constant mean curvature surfaces in Euclidean three-space J. Differ. Geom. 33 683-715
[4] Kapouleas N.(1987)The Yamabe problem Bull. Am. Math. Soc. (N.S.) 17 37-91
[5] Lee J.M.(1997)On a singularly perturbed elliptic equation Adv. Differ. Equ. 2 955-980
[6] Parker T.H.(1968)The minimal number of critical points of a function on a compact manifold and the Lusternic–Schnirelman category Invent. Math. 6 197-244
[7] Li Y.Y.(1991)Foliation by constant mean curvature spheres Pac. J. Math. 147 381-396
[8] Takens F.(undefined)undefined undefined undefined undefined-undefined
[9] Ye R.(undefined)undefined undefined undefined undefined-undefined

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