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:

- \(R\le \frac{c}{(T-t)^\alpha}\) for some small \(\alpha >0\),
- \(\int_M\mid R\mid^p<c\) 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 \(t\to T\).

## Publications

## Team Members

**Dr. Jiawei Liu**

Researcher

Otto-von-Guericke-Universität Magdeburg

jiawei.liu(at)ovgu.de

**Prof. Dr. Miles Simon**

Project leader

Otto-von-Guericke-Universität Magdeburg

miles.simon(at)ovgu.de