Loss of initial data under limits of Ricci flows

Abstract

We construct a sequence of smooth Ricci flows on $T^2$, with standard uniform $C/t$ curvature decay, and with initial metrics converging to the standard flat unit-area square torus $g_0$ in the Gromov-Hausdorff sense, with the property that the flows themselves converge not to the static Ricci flow $g(t)\equiv g_0$, but to the static Ricci flow $g(t)\equiv 2g_0$ of twice the area.

4 pages. This is the submitted version from 2019, but with updated references. Problem 1.2 can be answered using the theory in [19]

Cited by in corpus (2)

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