Journal of Differential Geometry

The heat equation shrinks embedded plane curves to round points

Matthew A. Grayson
Source: J. Differential Geom. Volume 26, Number 2 (1987), 285-314.
First Page: Show Hide
Primary Subjects: 53A04
Secondary Subjects: 35K99, 58G11
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jdg/1214441371
Mathematical Reviews number (MathSciNet): MR906392
Zentralblatt MATH identifier: 0667.53001

References

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Zentralblatt MATH: 0592.53002
Mathematical Reviews (MathSciNet): MR845704
Project Euclid: euclid.jdg/1214440025
[2] E. Calabi, Private Communication.
[3] M. Gage, An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50 (1983) 1225-1229.
Zentralblatt MATH: 0534.52008
Mathematical Reviews (MathSciNet): MR726325
Digital Object Identifier: doi:10.1215/S0012-7094-83-05052-4
Project Euclid: euclid.dmj/1077303497
[4] M. Gage, Curve shortening makes convex curves circular, Invent. Math. 76 (1984) 357-364.
Zentralblatt MATH: 0542.53004
Mathematical Reviews (MathSciNet): MR742856
Digital Object Identifier: doi:10.1007/BF01388602
[5] M. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geometry 23 (1986) 69-96.
Zentralblatt MATH: 0621.53001
Mathematical Reviews (MathSciNet): MR840401
Project Euclid: euclid.jdg/1214439902
[6] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
Zentralblatt MATH: 0556.53001
Mathematical Reviews (MathSciNet): MR772132
Project Euclid: euclid.jdg/1214438998
[7] M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, New York, 1967.
Zentralblatt MATH: 0153.13602
Mathematical Reviews (MathSciNet): MR219861

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Journal of Differential Geometry

Journal of Differential Geometry

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