# Einstein Hilbert action and Ricci flow on manifolds with boundary

**Time: **
Tue 2022-09-13 10.15 - 11.15

**Location: **
Room 3418, Lindstedtsvägen 25

**Language: **
English

**Participating: **
Rasmus Johansen Jouttijärvi, KTH

What are the natural boundary conditions to impose on the solutions of the Euler Lagrange equation associated with the total scalar curvature functional (The Einstein-Hilbert action)? Are they the same as those needed for the solutions of the Ricci flow?

Using the calculus of variations, it is possible to construct a set of boundary conditions for the Einstein Hilbert action, which are direct consequences of the first and second variation of the action. We will discuss the restrictiveness of these conditions and briefly cover the possibility of altering out initial functional, as to make the boundary conditions less restrictive.

We will attempt to apply the same techniques to discover the most natural boundary conditions for the Ricci-flow. Ultimately, we will show that it is possible to use the deTurck trick to reach statements about the short-time existence and regularity of a solution to the Ricci-flow equation, with regards to the chosen boundary conditions.