An extension procedure for manifolds with boundary
An extension procedure for manifolds with boundary
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DOI：
10.2140/pjm.2008.235.173
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发表时间：
2008-03
影响因子：
0.6
通讯作者：
J. Wong
中科院分区：
文献类型：
--
作者：
J. Wong
本文对带边界的黎曼流形引入了一个等距扩张过程，它保持了某些下曲率界，并产生了一个全测地边界。作为直接应用的建设，人们获得特别是体积上限，上限固有直径的边界，预紧性，和同胚有限性定理的某些类流形的边界，以及一个表征同伦的Gromov-Hausdorff限制这样一个类。
This paper introduces an isometric extension procedure for Riemannian manifolds with boundary, which preserves some lower curvature bound and produces a totally geodesic boundary. As immediate applications of this construction, one obtains in particular upper volume bounds, an upper intrinsic diameter bound for the boundary, precompactness, and a home-omorphism finiteness theorem for certain classes of manifolds with boundary , as well as a characterization up to homotopy of Gromov–Hausdorff limits of such a class.