Miles Simon: Ricci flow with L^p bounded scalar curvature.

In this talk, we show that localised, weighted curvature integral estimates for solutions to the Ricci flow in the setting of a smooth four dimensional Ricci flow or a closed \(n\)-dimensional Kähler Ricci flow always hold. These integral estimates improve and extend the integral curvature estimates shown in an earlier paper by the speaker. If \(M^4\) is closed and four dimensional, and the spatial \(L^p\) norm of the scalar curvature is uniformly bounded for some \(p>2\), for \(t\in [0,T)\), \(T<\infty\), then we show:
a) a uniform bound on the spatial \(L^2\) norm of the Riemannian curvature tensor for \(t\in [0,T)\),
b) uniform non-expanding and non-inflating estimates for \(t\in [0,T)\),
c) convergence to an orbifold as \(t \to T\),
d) existence of an extension of the flow to times \(t\in [0,T+\sigma)\) for some \(\sigma>0\) using the orbifold Ricci flow.
This is joint work with Jiawei Liu.