Singularities of convex hulls of smooth manifolds
Singularities of convex hulls of smooth manifolds
复制标题
光滑流形凸包的奇点
DOI：
10.1007/bf01079471
复制
发表时间：
1977
影响因子：
0.4
通讯作者：
V. Zakalyukin
中科院分区：
文献类型：
--
作者：
V. Zakalyukin
设M k是仿射空间rn的光滑紧子流形。M的凸包U (M)根据定义是包含M的闭半空间的交，该凸包的边界U (M)是一个非光滑拓扑流形。U (M)的奇异点出现在。最优控制理论和偏微分方程的研究。它们与R n中与M相切的元素的勒让德流形在仿射取向超平面的流形A n上的投影的奇异性密切相关。
Let M k be a smooth compact submanifold of the affine space R n. The convex hull U (M) of M is by definition the intersection of the closed halfspaces containing M. The boundary U (M) of this convex hull is a nonsmooth topological manifold.The singularities of U (M) appear-in the. theory of optimal control and in the study of partial differential equations. They are closely related to the singularities of the projections of the Legendre manifold of elements tangent to M onto the manifold A n of affine oriented hyperplanes in R n.