Flows in Flatland: A Romance of Few Dimensions

被引：0
|
作者：
Katz G. [1 ]
机构：
[1] 5 Bridle Path Circle, Framingham, 01701, MA
来源：
Arnold Mathematical Journal | 2017年 / 3卷 / 2期
关键词：
Boundary effects; Complexity; Convexity; Holography; Vector flows;
D O I：
10.1007/s40598-016-0059-1
中图分类号：
学科分类号：
摘要：
This paper is about gradient-like vector fields and flows they generate on smooth compact surfaces with boundary. We use this particular 2-dimensional setting to present and explain our general results about non-vanishing gradient-like vector fields on n-dimensional manifolds with boundary. We take advantage of the relative simplicity of 2-dimensional worlds to popularize our approach to the Morse theory on smooth manifolds with boundary. In this approach, the boundary effects take the central stage. © 2016, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
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页码：281 / 317
页数：36
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