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• W1522884065 abstract "We consider canonical metrics on Fano manifolds. First we introduce a norm-type functional on Fano manifolds, which has Kahler-Einstein or Kahler-Ricci soliton as its critical point and the Kahler-Ricci flow can be viewed as its (reduced) gradient flow. We then obtain a natural lower bound of this functional. As an application, we prove that Kahler-Ricci soliton, if exists, maximizes Perelman's $mu$-functional without extra assumptions. Second we consider a conjecture proposed by S.K. Donaldson in terms of $cK$-energy. Our simple observation is that $cF$-functional, as $cK$-energy, also integrates Futaki invariant. We then restate geodesic stability conjecture on Fano manifolds in terms of $cF$-functional. Similar pictures can also be extended to Kahler-Ricci soliton and modified $cF$-functional." @default.
• W1522884065 created "2016-06-24" @default.
• W1522884065 creator A5035903057 @default.
• W1522884065 date "2012-08-05" @default.
• W1522884065 modified "2023-09-27" @default.
• W1522884065 title "$cF$-functional and geodesic stability" @default.
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