Flows in Flatland: A Romance of Few Dimensions

@article{Katz2015FlowsIF,
  title={Flows in Flatland: A Romance of Few Dimensions},
  author={Gabriel Katz},
  journal={Arnold Mathematical Journal},
  year={2015},
  volume={3},
  pages={281-317}
}
  • G. Katz
  • Published 10 November 2015
  • Mathematics, Computer Science
  • Arnold Mathematical Journal
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… 
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9 Citations

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    Journal of Dynamics and Differential Equations
  • 2020
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