Journal of Differential Geometry

Flow of nonconvex hypersurfaces into spheres

Claus Gerhardt

Full-text: Open access

Article information

Source
J. Differential Geom. Volume 32, Number 1 (1990), 299-314.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214445048

Digital Object Identifier
doi:10.4310/jdg/1214445048

Mathematical Reviews number (MathSciNet)
MR1064876

Zentralblatt MATH identifier
0708.53045

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 35K15: Initial value problems for second-order parabolic equations 58G30

Citation

Gerhardt, Claus. Flow of nonconvex hypersurfaces into spheres. J. Differential Geom. 32 (1990), no. 1, 299--314. doi:10.4310/jdg/1214445048. https://projecteuclid.org/euclid.jdg/1214445048.


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References

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  • [2] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problemfor nonlinear second order elliptic equations, III; Functions of the eigenvalue of the Hessian, Acta Math. 155 (1985) 261-301.
  • [3] B. Chow, Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geometry 22 (1985) 117-138.
  • [4] B. Chow, Deforming convex hypersurfaces by the square root of the scalar curvature, Invent. Math. 87 (1987) 63-82.
  • [5] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
  • [6] G. Huisken, On the expansion of convex hypersurfacesby the inverse of symmetric curvature functions (to appear).
  • [7] N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Reidel, Dordrecht, 1987.
  • [8] J. Urbas, On the expansion of convex hypersurfaces by symmetric functions of their principal radii of curvature(to appear).