31

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 \(t\to T\).


Publications


    Team Members

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

    Wolfgang Meiser
    Doctoral student
    Otto-von-Guericke-Universität Magdeburg
    wolfgang.meiser(at)ovgu.de

    Prof. Dr. Miles Simon
    Project leader
    Otto-von-Guericke-Universität Magdeburg
    miles.simon(at)ovgu.de