On Ecker's local integral quantity at infinity for ancient mean curvature flows

Abstract

We point out that Ecker's local integral quantity agrees with Huisken's global integral quantity at infinity for ancient mean curvature flows if Huisken's one is finite on each time-slice. In particular, this means that the finiteness of Ecker's integral quantity at infinity implies the finiteness of the entropy at infinity.

11 pages. Corrected typos. Added some comments in Remark 1.4