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Solutions to Ricci flow whose scalar curvature is bounded in L^p.

The aim of this project is to understand singularities of the Ricci flow in four dimensions if we assume restrictions on the topology and / or geometry of the solutions we are considering.

In particular we will consider the cases:

1. $$R\le \frac{c}{(T-t)^\alpha}$$ for some small $$\alpha >0$$,
2.  $$\int_M\mid R\mid^p<c$$ for all $$t\in\left[0,T\right)$$ for some fixed large $$p>0$$,

where $$R$$ denotes the scalar curvature.

Using estimates / results / ideas from previous works we aim to show that in certain cases this restricts the type of singularities that may occur as $$t\to T$$.

## Team Members

Dr. Jiawei Liu
Researcher
Otto-von-Guericke-Universität Magdeburg
jiawei.liu(at)ovgu.de

Prof. Dr. Miles Simon