这就是庞加莱和瑟斯顿所说的三维流形：没有除了已发现的之外的任何流形存在。
This is what Poincaré and Thurston say about the world of 3-manifolds: there are no manifolds besides those which has been already discovered.
佩雷尔曼的工作揭示了瑞奇流定律——“三维板块构造理论”，它塑造了三维流形的世界。
Perelman's work revealed the laws of Hamilton's flow – the "3D-plate tectonics" which shaped the world of 3-manifolds.
佩雷尔曼的成就在于他实现了理查德·汉密尔顿的计划，从而揭示出三维流形空间的深邃的结构。
What Perelman has achieved is the fulfillment of Richard Hamilton's program, thus revealing a profound structure in the space of 3-manifolds.
目前工业界广泛使用的网格细分操作要求表达图形体的网格能够在三维空间中表达一个有效并且正确的二维流形。
Being widely used in industrial field recently, the subdivision operation based on mesh is required the original mesh of graph object which can present robust and valid 2-manifold in 3d Spaces.
本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。
This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.
本文通过构造形式级数的方式，给出了一种三维保测度映射系统中一维不变流形和二维不变流形的计算方法。
In the paper researches on a three-dimensional measure-Preserving mapping system are made, which is the three-dimensional extension of the Keplerian map-ping.
本文通过构造形式级数的方式，给出了一种三维保测度映射系统中一维不变流形和二维不变流形的计算方法。
In the paper researches on a three-dimensional measure-Preserving mapping system are made, which is the three-dimensional extension of the Keplerian map-ping.
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