Short time existence on normalized Kahler Ricci flow - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T14:11:40Z http://mathoverflow.net/feeds/question/99447 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99447/short-time-existence-on-normalized-kahler-ricci-flow Short time existence on normalized Kahler Ricci flow Hassan Jolany 2012-06-13T13:48:13Z 2012-07-12T00:06:11Z <p>How we can prove the short time existence for Kahler Ricci flow on compact manifolds. I know that by linearization and Detork's trick we can prove the short time existence for Ricci flow, but for proving on Kahler Ricci flow we have to use of second order parabolic equations. Of course on noncompact manifolds I have seen a nice proof but In this question I mean on compact manifolds.</p> http://mathoverflow.net/questions/99447/short-time-existence-on-normalized-kahler-ricci-flow/99469#99469 Answer by Deane Yang for Short time existence on normalized Kahler Ricci flow Deane Yang 2012-06-13T16:19:09Z 2012-06-13T16:19:09Z <p>First, the Kahler-Ricci flow <em>is</em> the Ricci flow applied to a Kahler metric (which is a Riemannian metric), so any theorem and proof for local time existence of the Ricci flow applies to the Kahler-Ricci flow.</p> <p>Second, as far as I know, any proof for short time existence that works for noncompact manifolds will work without any change for a compact manifold (without boundary).</p> <p>Third, as Otis has pointed out, the Kahler-Ricci flow can be written as an honest nonlinear parabolic PDE for the potential. If you believe that a linear parabolic PDE can be solved, then the nonlinear theorem is easily proved using energy integral estimates and the implicit function theorem.</p>