3-流形中最小面积曲面的拟正规性与 PL 逼近
Quasi Normality and PL Approximation of Least Area Surfaces in 3-Manifolds
AI总结：
本文研究欧氏或双曲 3-流形中的最小面积曲面，提出拟正规曲面概念，证明其相对精细肥胖三角剖分的拟正规性，并构造收敛且逼近面积的平坦关联曲面序列。
摘要：
本文给出了嵌入于欧氏或双曲 3-流形中的最小面积曲面与正规曲面之间的关系。文中引入了正规曲面的一种放宽形式，称为拟正规曲面，并证明在适当条件下，对于该 3-流形的足够精细的肥胖三角剖分，每个嵌入的最小面积曲面都是拟正规的。此外，文中证明最小面积曲面与此类足够精细三角剖分的四面体的交，即使不像正规曲面情形那样简单，也同样具有良好性质。最后，文中证明，当把最小面积曲面视为拟正规曲面时，它会产生一系列分片平坦曲面，称为平坦关联曲面，并且该序列收敛于给定的最小面积曲面，同时逼近其面积。
英文摘要：
This} paper presents relations between least area and normal surfaces, embedded in either a Euclidean or hyperbolic $3$-manifold. A relaxed version of normal surfaces, termed quasi-normal, is introduced, and it is shown that under appropriate conditions, every embedded least area surface is quasi-normal with respect to a fine enough fat triangulation of the $3$-manifold. In addition, it is shown that the intersections of a least area surface with the tetrahedra of such fine enough triangulation, even when not as simple as in the case of normal surfaces, are also well behaved. Finally, it is shown that a least area surface, when considered as a quasi normal surface, gives rise to a sequence of piecewise flat surfaces termed as flat-associated surfaces, and this sequence converges to the given least area surface and approximates its area.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
