Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature
Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature
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DOI：
10.4310/jdg/1090348111
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发表时间：
2001-02
影响因子：
2.5
通讯作者：
M. Ghomi
中科院分区：
文献类型：
--
作者：
M. Ghomi
构造具有指定子流形和切平面的正曲率光滑闭超曲面。进一步，我们通过Monge-Amp方程、凸多面体的光滑以及Hadamard的卵圆定理在有边界的超曲面上的推广，在边值问题上得到了一些应用。
We construct smooth closed hypersurfaces of positive curvature with prescribed submanifolds and tangent planes. Further, we develop some applications to boundary value problems via Monge-Amp ere equations, smoothing of convex polytopes, and an extension of Hadamard's ovaloid theorem to hypersurfaces with boundary.