Journal of Differential Geometry

Flow of nonconvex hypersurfaces into spheres

Claus Gerhardt

Full-text: Open access

Article information

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

First available in Project Euclid: 26 June 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation


  • [1] K. A. Brakke, The motion of a surface by its mean curvature, Math. Notes, No. 20, Princeton Univ. Press, Princeton, NJ, 1977.
  • [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).