کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1894881 | 1044252 | 2012 | 10 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Results on the existence of the Yamabe minimizer of Mm×Rn Results on the existence of the Yamabe minimizer of Mm×Rn](/preview/png/1894881.png)
We let (Mm,g)(Mm,g) be a closed smooth Riemannian manifold with positive scalar curvature SgSg, and prove that the Yamabe constant of (M×Rn,g+gE) (n,m≥2n,m≥2) is achieved by a metric in the conformal class of (g+gE)(g+gE), where gEgE is the Euclidean metric. We do this by showing that the Yamabe functional of (M×Rn,g+gE) is improved under Steiner symmetrization with respect to MM, and so, the dependence on Rn of the Yamabe minimizer of (M×Rn,g+gE) is radial.
► Let (Mm,g)(Mm,g) be a compact, smooth, Riemannian manifold with positive scalar curvature.
► Let (N,h)=(MmxRn,g+gE), with n,m>1n,m>1, and gEgE the Euclidean metric.
► Steiner symmetrization with respect to MM improves the Yamabe functional of (N,h)(N,h).
► The Yamabe minimizer of (N,h)(N,h) exists, and is positive and smooth.
► The dependence on RnRn of the Yamabe minimizer of (N,h)(N,h) is radial.
Journal: Journal of Geometry and Physics - Volume 62, Issue 1, January 2012, Pages 11–20