Geometric Expansion of Starshaped Plane Curves

Communications in Analysis and Geometry

Volumn 4, Issue 3, 1996, Pages 459-480

  Tsai, Dong Ho ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012873685     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.1996.v4.n3.a5     Document Type: Article

References (20)

1. Andrews, B. (1993) thesis, Evolving convex hypersurfaces, The Australian National University.
2. Chow, B. (1995) Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations, to appear in Comm. Anal. and Geom. 1996/1997.
3. Chow, B., Gulliver, R. (1994) Aleksandrov reflection and nonlinear evolution equations, I: The n-sphere and n-ball, to appear.
4. Chow, B., Gulliver, R. (1995) Aleksandrov reflection and geometric evolution of embedded hypersurfaces, in preparation.
5. Chow, B., Tsai, D.H. (1994) Geometric expansion of convex plane curves, to appear in J. Diff. Geom. 1996.
6. Chow, B., Tsai, D.H. (1995) Expansion of convex hypersurfaces by nonhomogeneous functions of curvature, in preparation.
7. n, to appear in Comm. Anal. and Geom. 1996/1997.
8. Chow, B., Liou, L.P., Tsai, D.H. (1995) Expansion of embedded plane curves with turning angle greater than -π, to appear in Inventiones Mathematicae 1996.
9. Gage, M., Hamilton, R. S. (1986) The heat equation shrinking convex plane curves, J. Diff. Geom. 23, 69-96.
10. Gerhardt, C. (1990) Flow of nonconvex hypersurfaces into spheres, J. Diff. Geom. 32, 299-314.
11. Hamilton, R.S. (1982) Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17, 255-306.
12. Hamilton, R.S. (1986) Four-manifolds with positive curvature operator, J. Diff. Geom. 24, 153-179.
13. Huisken, G. (1984) Flow by mean curvature of convex hypersurfaces into spheres, J. Diff. Geom. 20, 237-268.
14. Huisken, G. (1988) On the expansion of convex hypersurfaces by the inverse of symmetric functions, preprint.
15. Krylov, N. V., Safonov, M. V. (1980) Certain properties of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 40, 161-175, English tsansl., Math. USSR Izv. 16 (1981) 151-164.
16. Krylov, N. V., Safonov, M. V. (1980) Certain properties of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 40, 161-175, English tsansl., Math. USSR Izv. 16 (1981) 151-164.
17. Tsai, D.H. (1995) Geometric expansion of immersed convex plane curves, in preparation.
18. Tso, K. (1985) Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure and Appl. Math. 38, 867-882.
19. Urbas, J.I.E. (1991) An expansion of convex hypersurfaces, J. Diff. Geom. 33, 91-125; (1992) Correction to, ibid. 35, 763-765.
20. Urbas, J.I.E. (1990) On the expansion of star shaped hypersurfaces by symmetric functions of their principal curvatures, Math. Z. 205, 355-372.