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
    Otto-von-Guericke-Universität Magdeburg

    Prof. Dr. Miles Simon
    Project leader
    Otto-von-Guericke-Universität Magdeburg