• Corpus ID: 2394148

Minimal number of self-intersections of the boundary of an immersed surface in the plane

@article{Guth2009MinimalNO,
  title={Minimal number of self-intersections of the boundary of an immersed surface in the plane},
  author={Larry Guth},
  journal={arXiv: Differential Geometry},
  year={2009}
}
  • L. Guth
  • Published 18 March 2009
  • Mathematics
  • arXiv: Differential Geometry
We find the minimal number of self-intersections of the boundary of a surface of genus g generically immersed in the plane. 
View PDF on arXiv
3 Citations
Background Citations
1

3 Citations

Flows in Flatland: A Romance of Few Dimensions

  • G. Katz
  • Mathematics, Computer Science
  • 2015
This paper uses the relative simplicity of 2-dimensional worlds to popularize the approach to the Morse theory on smooth manifolds with boundary, and takes advantage of the boundary effects to take the central stage.

Flows in Flatland: A Romance of Few Dimensions

  • G. Katz
  • Mathematics, Computer Science
    Arnold Mathematical Journal
  • 2016
This paper uses the relative simplicity of 2-dimensional worlds to popularize the approach to the Morse theory on smooth manifolds with boundary, and takes advantage of the boundary effects to take the central stage.

Stratified Convexity & Concavity of Gradient Flows on Manifolds with Boundary

As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main…

References

SHOWING 1-3 OF 3 REFERENCES

On regular closed curves in the plane

© Foundation Compositio Mathematica, 1937, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…

Singularities, Expanders, and Topology of Maps, preprint

  • Singularities, Expanders, and Topology of Maps, preprint

E-mail address: lguth@math.toronto.edu

  • E-mail address: lguth@math.toronto.edu