Evolving plane curves by curvature in relative geometries II
Michael E. Gage and Yi Li
Source: Duke Math. J. Volume 75, Number 1
(1994), 79-98.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077287411
Mathematical Reviews number (MathSciNet): MR1284816
Zentralblatt MATH identifier: 0811.53033
Digital Object Identifier: doi:10.1215/S0012-7094-94-07503-0
References
[An1] S. Angenent, Parabolic equations for curves on surfaces. I. Curves with $p$-integrable curvature, Ann. of Math. (2) 132 (1990), no. 3, 451–483.
Mathematical Reviews (MathSciNet): MR91k:35102
Zentralblatt MATH: 0789.58070
Digital Object Identifier: doi:10.2307/1971426
JSTOR: links.jstor.org
[An2] S. Angenent, Parabolic equations for curves on surfaces. II. Intersections, blow-up and generalized solutions, Ann. of Math. (2) 133 (1991), no. 1, 171–215.
Mathematical Reviews (MathSciNet): MR92b:58039
Zentralblatt MATH: 0749.58054
Digital Object Identifier: doi:10.2307/2944327
JSTOR: links.jstor.org
[An3] S. Angenent, On the formation of singularities in the curve shortening flow, J. Differential Geom. 33 (1991), no. 3, 601–633.
Mathematical Reviews (MathSciNet): MR92c:58016
Zentralblatt MATH: 0731.53002
Project Euclid: euclid.jdg/1214446558
[An4] S. Angenent, Nonlinear analytic semiflows, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 1-2, 91–107.
Mathematical Reviews (MathSciNet): MR91c:34085
Zentralblatt MATH: 0723.34047
[AG] S. Angenent and M. Gurtin, Multiphase thermomechanics with interfacial structure. II. Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108 (1989), no. 4, 323–391.
Mathematical Reviews (MathSciNet): MR91d:73004
Zentralblatt MATH: 0723.73017
Digital Object Identifier: doi:10.1007/BF01041068
[EG] C. Epstein and M. Gage, The curve shortening flow, Wave motion: theory, modelling, and computation (Berkeley, Calif., 1986), Math. Sci. Res. Inst. Publ., vol. 7, Springer, New York, 1987, Proceedings of a Conference in Honor of the 60th Birthday of Peter D. Lax, pp. 15–59.
Mathematical Reviews (MathSciNet): MR89f:58128
Zentralblatt MATH: 0645.53028
[Fi] W. Firey, Shapes of worn stones, Mathematika 21 (1974), 1–11.
Mathematical Reviews (MathSciNet): MR50:14487
Zentralblatt MATH: 0311.52003
Digital Object Identifier: doi:10.1112/S0025579300005714
[Ga1] M. Gage, An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50 (1983), no. 4, 1225–1229.
Mathematical Reviews (MathSciNet): MR85d:52007
Zentralblatt MATH: 0534.52008
Digital Object Identifier: doi:10.1215/S0012-7094-83-05052-4
Project Euclid: euclid.dmj/1077303497
[Ga2] M. Gage, On the size of the blow-up set for a quasilinear parabolic equation, Geometry and nonlinear partial differential equations (Fayetteville, AR, 1990) ed. V. Oliker, Contemp. Math., vol. 127, Amer. Math. Soc., Providence, RI, 1992, pp. 41–58.
Mathematical Reviews (MathSciNet): MR93c:35066
Zentralblatt MATH: 0770.35029
[Ga3] M. Gage, Evolving plane curves by curvature in relative geometries, preprint.
Mathematical Reviews (MathSciNet): MR1248680
Digital Object Identifier: doi:10.1215/S0012-7094-93-07216-X
Project Euclid: euclid.dmj/1077289427
[GH] M. Gage and R. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom. 23 (1986), no. 1, 69–96.
Mathematical Reviews (MathSciNet): MR87m:53003
Zentralblatt MATH: 0621.53001
Project Euclid: euclid.jdg/1214439902
[Gr1] M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. 26 (1987), no. 2, 285–314.
Mathematical Reviews (MathSciNet): MR89b:53005
Zentralblatt MATH: 0667.53001
Project Euclid: euclid.jdg/1214441371
[Ha1] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153–179.
Mathematical Reviews (MathSciNet): MR87m:53055
Zentralblatt MATH: 0628.53042
Project Euclid: euclid.jdg/1214440433
[Ha2] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1988, pp. 237–262.
Mathematical Reviews (MathSciNet): MR89i:53029
Zentralblatt MATH: 0663.53031
[Ha3] R. S. Hamilton, Lecture Notes on Heat Equations in Geometry, Honolulu, Hawaii (1989), Contemp. Math., Amer. Math. Soc., Providence, to appear.
[PW] M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1967.
Mathematical Reviews (MathSciNet): MR36:2935
Zentralblatt MATH: 0153.13602
[Sa1] L. Santalo, Integral geometry and geometric probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.
Mathematical Reviews (MathSciNet): MR55:6340
Zentralblatt MATH: 0342.53049
[Ta1] J. Taylor, Constructions and conjectures in crystalline non-differential geometry, in Proceedings of Conference in Differential Geometry, Rio de Janeiro, 1988, to appear.
[Ts1] K. Tso, Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math. 38 (1985), no. 6, 867–882.
Mathematical Reviews (MathSciNet): MR87e:53009
Zentralblatt MATH: 0612.53005
Digital Object Identifier: doi:10.1002/cpa.3160380615
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