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.

arXiv comment4 pages. This is the submitted version from 2019, but with updated references. Problem 1.2 can be answered using the theory in [19]

References in corpus (3)

• Existence of Ricci flows of incomplete surfaces
• Uniqueness of Instantaneously Complete Ricci flows
• Short-time existence of the Ricci flow on complete, non-collapsed $3$-manifolds with Ricci curvature bounded from below

Cited by in corpus (2)

• Convexity of 2-convex translating and expanding solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$
• Smoothing a measure on a Riemann surface using Ricci flow