The WPIC1 Ricci-flow existence conjecture

Let (Mn,g0)(M^n,g_0) be a complete WPIC1 manifold with n3n\geq 3. WPIC1 Ricci-flow existence conjecture. There exists a complete WPIC1 Ricci flow g(t)g(t) on MM for t[0,T)t\in[0,T), for some T>0T>0, with g(0)=g0g(0)=g_0. This conjecture is the key Ricci-flow existence step for applying smoothing to the topology problem on complete noncompact manifolds. In dimension three it asserts that a complete metric with nonnegative Ricci curvature should induce a complete Ricci-flow evolution; the general statement remains open in the supplied discussion.

Sources & referencesView supporting material

Primary source

Peter M. Topping, “Ricci flow and PIC1”, arXiv:2309.00596 (2023).

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