I'm currently at a Differential Geometry meeting and there is a minicourse on positively curved Riemannian manifolds. There, we were told that a technique to construct such manifolds is a Cheeger deformation, which (if I understood correctly) is a generalization of a oneparameter family of surfaces of revolution given by $\frac{f}{\lambda f + 1}$, where $f$ is the curve that generates a surface of revolution in Euclidean space and $\lambda$ is a positive parameter that varies over $[0,\infty)$. Can anyone tell me what is the concrete definition of a Cheeger deformation and how are they used to construct manifolds of positive (or nonnegative, perhaps; I don't remember) curvature? Thanks a lot.
