Rigidity of Entire self-shrinking solutions to curvature flows

Details Rigidity of Entire self-shrinking solutions to curvature flows Rigidity of Entire self-shrinking solutions to curvature flows

2010-03-16

arxiv.org/abs/1003.3246v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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 K\"ahler Ricci flow.

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