Generic Transversality of Minimal Submanifolds
Generic Transversality of Minimal Submanifolds
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最小子流形的一般横截性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
B. White
中科院分区：
文献类型：
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作者：
B. White
设$N$是具有光滑黎曼度量的光滑流形，$Gamma$是$N$的光滑子流形。证明了对于一般的(在Baire范畴意义下)光滑度量$g$共形到$g_0$，如果$F$是闭流形到N中的任何单$g$-极小浸入，则$F$横切于$Gamma$，且$F$是自横切的.用“强横向”和“强自横向”代替“横向”和“自横向”，这个定理仍然成立。该定理也适用于常平均曲率的超曲面，或者更一般地，具有规定的平均曲率的超曲面。
Suppose that $N$ is a smooth manifold with a smooth Riemannian metric $g_0$, and that $Gamma$ is a smooth submanifold of $N$. This paper proves that for a generic (in the sense of Baire category) smooth metric $g$ conformal to $g_0$, if $F$ is any simple $g$-minimal immersion of a closed manifold into N, then $F$ is transverse to $Gamma$ and $F$ is self-transverse. The theorem remains true with "transverse" and "self-transverse" replaced by "strongly transverse" and "strongly self-transverse". The theorem also holds for hypersurfaces of constant mean curvature or, more generally, of prescribed mean curvature.
论极小极大理论中的重数一猜想
影响因子：
4.9
作者：
Zhou, X
通讯作者：
Zhou, X