112 research outputs found
A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow
It is a theorem of S. Bando that if is a solution to the Ricci flow on
a compact manifold , then is real-analytic for each . In
this note, we extend his result to smooth solutions on open domains
Rigidity of asymptotically conical shrinking gradient Ricci solitons
We show that if two gradient Ricci solitons are asymptotic along some end of
each to the same regular cone, then the soliton metrics must be isometric on
some neighborhoods of infinity of these ends. Our theorem imposes no
restrictions on the behavior of the metrics off of the ends in question and in
particular does not require their geodesic completeness. As an application, we
prove that the only complete connected gradient shrinking Ricci soliton
asymptotic to a rotationally symmetric cone is the Gaussian soliton on R^n.Comment: 44 page
Ricci flow and the holonomy group
We prove that the restricted holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract in finite time; it follows, then, from an earlier result of Hamilton that the holonomy group is exactly preserved by the equation. In particular, a solution to the Ricci flow may be K\"{a}hler or locally reducible (as a product) at if and only if the same is true of at times
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