Shapes of embedded minimal surfaces

Colding TH; Minicozzi WP

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Shapes of embedded minimal surfaces

机译：嵌入的最小曲面的形状

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Surfaces that locally minimize area have been extensively used to model physical phenomena, including soap films, black holes, compound polymers, protein folding, etc. The mathematical field dates to the 1740s but has recently become an area of intense mathematical and scientific study, specifically in the areas of molecular engineering, materials science, and nanotechnology because of their many anticipated applications. In this work, we show that all minimal surfaces are built out of pieces of the surfaces in Figs. 1 and 2.

机译：局部最小化的表面已被广泛用于模拟物理现象，包括肥皂膜，黑洞，复合聚合物，蛋白质折叠等。数学领域可追溯至1740年代，但最近已成为广泛的数学和科学研究领域，特别是在分子工程，材料科学和纳米技术领域具有广泛的应用前景。在这项工作中，我们显示了所有最小的表面都是由图1和2中的表面组成。 1和2。

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来源
《Proceedings of the National Academy of Sciences of the United States of America》 |2006年第30期|p. 11106-11111|共6页
作者
Colding TH; Minicozzi WP;
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作者单位

MIT, Dept Math, Cambridge, MA 02139 USA;

NYU, Courant Inst Math Sci, New York, NY 10012 USA;

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收录信息美国《科学引文索引》(SCI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类自然科学总论;
关键词
FIXED GENUS; SPACE; UNIQUENESS; DISKS;

机译：固定类;空间;唯一性;磁盘;

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机译：嵌入在R-3中的周期性最小曲面来自单周期的Scherk最小表面
2. THE SPACES OF INDEX ONE MINIMAL SURFACES AND STABLE CONSTANT MEAN CURVATURE SURFACES EMBEDDED IN FLAT THREE MANIFOLDS [J] . Ritore M., Ros A. Transactions of the American Mathematical Society . 1996,第1期

机译：平面三流形中包含的索引一最小曲面和稳定的恒定均值曲面的空间
3. Thermal characterization of 3D-Printed lattices based on triply periodic minimal surfaces embedded with organic phase change material [J] . Zahid Ahmed Qureshi, Salah Addin Burhan Al Omari, Emad Elnajjar, Case Studies in Thermal Engineering . 2020,第a期

机译：基于嵌入有机相变材料的三个周期性最小表面的3D印刷格子热表征
4. Facade shaping inspired by Scherk's minimal surfaces [C] . Jan Pelczynski, Pawel Wawruch R-S-P Seminar on Theoretical Foundation of Civil Engineering (24RSP) . 2015

机译：由Scherk的最小表面感到灵感的立面塑造
5. Embedded minimal surfaces of finite topology and one end. [D] . Breiner, Christine. 2009

机译：有限拓扑和一端的嵌入式最小曲面。
6. Shapes of embedded minimal surfaces [O] . Tobias H. Colding, William P. Minicozzi II 2006

机译：嵌入的最小曲面的形状
7. Shapes of embedded minimal surfaces [O] . Colding, Tobias H., Minicozzi, William P. 2006

机译：嵌入的最小曲面的形状

Shapes of embedded minimal surfaces

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