An expansion of convex hypersurfaces

Journal of Differential Geometry

Volumn 33, Issue 1, 1991, Pages 91-125

  Urbas, John I E ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972517049     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214446031     Document Type: Article

References (18)

1. T. Aubin, Nonlinear analysis on manifolds, Monge-Ampère equations, Springer, Berlin, 1982.
2. T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Springer, Berlin, 1934.
3. K. A. Brakke, The motion of a surface by its mean curvature, Math. Notes, Princeton Univ. Press, Princeton, NJ, 1978.
4. L. Caffarelli, L. Nirenberg & J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985) 261-301.
5. B. Chow, Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geometry 22 (1985) 117-138.
6. B. Chow, Deforming convex hypersurfaces by the square root of the scalar curvature, Invent. Math. 87 (1987) 63-82.
7. W. J. Firey, Shapes of worn stones, Mathematika 21 (1974) 1-11.
8. M. Gage & R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geometry 23 (1986) 69-96.
9. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982) 255-306.
10. R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geometry 24 (1986) 153-179.
11. G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
12. G. Huisken, On the expansion of convex hypersurfaces by the inverse of symmetric curvature functions, to appear.
13. N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Reidel, Dordrecht, 1987.
14. N. V. Krylov & M. V. Safonov, A certain property of solutions ofparabolic equations with measurable coefficients, Izv. Akad. Nauk 40 (1980) 161-175; English transl., Math. USSR Izv. 16 (1981) 151-164.
15. O. A. Ladyzhenskaya, V. A. Solonnikov & N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl., Amer. Math. Soc., Providence, RI, 1968.
16. D. S. Mitrinović, Analytic inequalities, Springer, Berlin, 1970.
17. A. V. Pogorelov, The Minkowski multidimensional problem, Wiley, New York, 1978.
18. K. Tso, Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math. 38 (1985) 867-882.