2018/05/23 by Timothy Carson, Carson, Timothy
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1805.09401
We prove the existence of Ricci flow starting from a class of metrics with\nunbounded curvature, which are doubly-warped products over an interval with a\nspherical factor pinched off at an end. These provide a forward evolution from\nsome known and conjectured finite-time local singularities of Ricci flow,\ngeneralizing previous examples. The class also includes metrics with\nnon-compact singular ends which become instantaneously compact. Furthermore, we\nprove local stability of the forward evolution, which allows us to glue it to\nother manifolds and create a forward evolution from spaces which are not\nglobally warped products.\n