2023/10/11 by Stephen Lynch, Lynch, Stephen · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2310.07369
We prove a differential Harnack inequality for noncompact convex hypersurfaces flowing with normal speed equal to a symmetric function of their principal curvatures. This extends a result of Andrews for compact hypersurfaces. We assume that the speed of motion is one-homogeneous, uniformly elliptic, and suitably 'uniformly' inverse-concave as a function of the principal curvatures. In addition, we assume the hypersurfaces satisfy pointwise scaling-invariant gradient estimates for the second fundamental form. For many natural flows all of these hypotheses are met by any ancient solution which arises as a blow-up of a singularity.