Ricci flow from some spaces with asymptotically cylindrical singularities
Differential Geometry
2018-05-25 v1
Abstract
We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some known and conjectured finite-time local singularities of Ricci flow, generalizing previous examples. The class also includes metrics with non-compact singular ends which become instantaneously compact. Furthermore, we prove local stability of the forward evolution, which allows us to glue it to other manifolds and create a forward evolution from spaces which are not globally warped products.
Cite
@article{arxiv.1805.09401,
title = {Ricci flow from some spaces with asymptotically cylindrical singularities},
author = {Timothy Carson},
journal= {arXiv preprint arXiv:1805.09401},
year = {2018}
}