On M. Mueter's Ph.D. Thesis on Cheeger deformations

TL;DR

This paper summarizes Michael Mueter's Ph.D. thesis on Cheeger deformations, focusing on their curvature properties and significance in constructing manifolds with non-negative or positive curvature.

Contribution

It provides an accessible overview of Mueter's detailed analysis of Cheeger deformations, which were previously known only to a few experts and not widely published.

Findings

Detailed properties of Cheeger deformations analyzed

Insights into curvature enhancement techniques

Potential applications in geometric constructions

Abstract

These are notes of a talk I gave in a seminar at the University of Pennsylvania summarizing results in the Ph.D. thesis of Michael Mueter obtained under the direction of Wolfgang Meyer at the University of Muenster. His thesis on "Kruemmungserhoehende Deformationen mittels Gruppenaktionen" examines in detail curvature properties of so called Cheeger deformations. Such deformations have been a crucial ingredient in non-negative and positive curvature constructions. His thesis contains a wealth of interesting properties of such deformations, but since it was never published, is only known to a few experts. I have no intention to publish these notes, but post them as a service to the public. A scanned version of his thesis (written in German) is available on my homepage.