Entropy and a convergence theorem for Gauss curvature flow in high dimension

  • Pengfei Guan

    McGill University, Montreal, Canada
  • Lei Ni

    University of California at San Diego, La Jolla, USA

Abstract

We prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in -topology to a smooth strictly convex soliton as goes to infinity is obtained as a consequence of these estimates together with an earlier result of Andrews. The estimates are established via the study of an entropy functional for convex bodies.

Cite this article

Pengfei Guan, Lei Ni, Entropy and a convergence theorem for Gauss curvature flow in high dimension. J. Eur. Math. Soc. 19 (2017), no. 12, pp. 3735–3761

DOI 10.4171/JEMS/752