Timeline for How can we formulate maximal time $T$ in Hyperbolic Kahler Ricci ﬂow

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Jul 8, 2014 at 12:45	history	edited	user21574	CC BY-SA 3.0	edited title
Apr 5, 2013 at 11:28	history	edited	user21574		edited tags
Sep 20, 2012 at 19:42	history	edited	user21574		edited tags; edited tags
Sep 2, 2012 at 3:15	comment	added	Deane Yang		YangMills, I think there is at least a chance that the reduction to a scalar equation still works for the hyperbolic flow. But you're right that there would be no analogue to the maximum principle for a hyperbolic flow (which is usually oscillatory), and this makes it unlikely that a result as good as Tian-Zhang holds.
Sep 2, 2012 at 3:04	history	edited	YangMills		edited tags
Sep 2, 2012 at 3:03	comment	added	YangMills		Indeed it sounds like a highly nontrivial problem. The key to the Tian-Zhang theorem are $L^\infty$ estimates on the Kahler potential and its time derivative which are obtained by maximum principle. First of all, can the hyperbolic Kahler Ricci flow be reduced to a scalar hyperbolic equation? If not, then most likely there is no such neat result for this flow. If yes, you would still need to find ways to replace the maximum principle arguments for the hyperbolic scalar equation that you'd get.
Sep 2, 2012 at 0:16	comment	added	Deane Yang		The Kahler-Ricci flow behaves particularly well as a PDE, making it possible but still not easy to characterize the existence time in terms of global geometric invariants. It's possible that the hyperbolic Kahler-Ricci flow is similar, but since it has not been studied that much yet, I suspect your question is a good challenging research question beyond the scope of MathOverflow. A good way to start is to see what properties, if any, of the Kahler-Ricci flow also hold for the hyperbolic Kahler-Ricci flow.
Sep 1, 2012 at 22:38	history	asked	user21574	CC BY-SA 3.0