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# A gap theorem and some uniform estimates for Ricci flows on homogeneous spaces

## Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016

May 06, 2016 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Miles Simon (Otto-von-Guericke-Universität Magdeburg)
Location: MSRI: Simons Auditorium
Tags/Keywords
• complex geometry

• Riemannian geometry

• geometric analysis

• geometric flow

• Ricci flow

• curvature estimates

• uniform estimate

• Cheeger inequalities

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

We prove a gap theorem for homogeneous spaces : If the norm of the Riemannian curvature is one, then the norm of the Ricci curvature is larger than $\ep(n)$, where $\ep(n)$ is a positive constant depending only on the dimension $n$ of the homogeneous space. This is used to show that solutions with finite extinction time are Type I, immortal solutions are Type III and ancient solutions are Type I, where all the constants involved depend  only on the dimension $n$.

This is joint work with Christoph Böhm (University of Münster), Ramiro Lafuente (University of Münster)

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