Curve shortening on surfaces

Michael E. Gage

Annales scientifiques de l'École Normale Supérieure (1990)

  • Volume: 23, Issue: 2, page 229-256
  • ISSN: 0012-9593

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Gage, Michael E.. "Curve shortening on surfaces." Annales scientifiques de l'École Normale Supérieure 23.2 (1990): 229-256. <http://eudml.org/doc/82272>.

@article{Gage1990,
author = {Gage, Michael E.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {curve shortening flow; 2-dimensional surface; Embedded curves},
language = {eng},
number = {2},
pages = {229-256},
publisher = {Elsevier},
title = {Curve shortening on surfaces},
url = {http://eudml.org/doc/82272},
volume = {23},
year = {1990},
}

TY - JOUR
AU - Gage, Michael E.
TI - Curve shortening on surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1990
PB - Elsevier
VL - 23
IS - 2
SP - 229
EP - 256
LA - eng
KW - curve shortening flow; 2-dimensional surface; Embedded curves
UR - http://eudml.org/doc/82272
ER -

References

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  1. [A] V. I. ARNOLD, Ordinary Differential Equations, M.I.T. Press, 1973. Zbl0296.34001MR50 #13679
  2. [An1] S. ANGENENT, The Zeroset of a Solution of a Parabolic Equation (J. reine angew. Math., Vol. 390, 1988, pp. 79-96). Zbl0644.35050MR89j:35015
  3. [An2] S. ANGENENT, Nodal Properties of Solutions of Parabolic Equations, for the Proceedings of the Conference on Nonlinear PDE's held in Provo, Utah, March 3-7, 1987. 
  4. [G1] M. GAGE, An Isoperimetric Inequality with Applications to Curve Shortening (Duke Math. J., Vol. 50, No. 4, 1983, pp. 1225-1229). Zbl0534.52008MR85d:52007
  5. [G2] M. GAGE, Curve Shortening Makes Convex Curves Circular (Invent. Math., Vol. 76, 1984, pp. 357-364). Zbl0542.53004MR85i:52004
  6. [G3] M. GAGE, On an Area-preserving Evolution Equation for Plane Curves (Contemporary Mathematics, Vol. 51, 1986. Zbl0608.53002MR87g:53003
  7. [G-H] M. GAGE and R. HAMILTON, The Shrinking of Convex Plane Curves by the Heat Equation (J. Diff. Geom., Vol. 23, 1986, pp. 69-96). Zbl0621.53001MR87m:53003
  8. [A-L] U. ABRESCH and J. LANGER, The Normalized Curve Shortening Flow and Homothetic Solutions (J. Diff. Geom., Vol. 23, 1986, pp. 175-196). Zbl0592.53002MR88d:53001
  9. [E-G] Charles EPSTEIN and M. GAGE, The curve shortening flow, in Wave motion : theory, modelling, and computation, Proceedings of a Conference in honor of the 60th birthday of Peter D. Lax, MSRI Publications, Springer-Verlag, 1987. Zbl0645.53028
  10. [Gr1] M. GRAYSON, The heat Equation Shrinks Embedded Plane Curves to Round Points (J. of Diff. Geom., Vol. 26, 1987, pp. 285-314). Zbl0667.53001MR89b:53005
  11. [Gr2] M. GRAYSON, Shortening Embedded Curves (Annals of Mathematics, Vol. 129, 1989, pp. 71-111). Zbl0686.53036MR90a:53050

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