Rigidity of Entire self-shrinking solutions to curvature flows

Abstract

We show that (a) any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in ${\mathbb{C}}^m$ with the Euclidean metric is flat; (b) any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in ${\mathbb{C}}^m$ with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the Kähler Ricci flow.

10 pages

References in corpus (2)

• Entire self-similar solutions to Lagrangian Mean curvature flow
• Lagrangian Mean Curvature flow for entire Lipschitz graphs II