Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
The author applies the Aleksandrov reflection principle in order to derive gradient estimates for geometric evolution equations. He considers two classes of examples. The first part deals with hypersurfaces moving in the direction of their normals whose speed is a function of the principal curvatures. The author proves a gradient estimate in the case of starshaped hypersurfaces expanding by non-homogeneous functions of curvature. In the second part on degenerate parabolic flows of locally conformally flat metrics, the author obtains a uniform gradient estimate for the logarithm of the conformal factor, extending a result of \textit{R.-G. Ye} [J. Differ. Geom. 39, 35-50 (1994; Zbl 0846.53027)] on the Yamabe flow.
scientific article; zbMATH DE number 1127780