| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
cscK metric is not directly expressed as a solution of a Monge-Ampere equation. However, cscK metric is a critical point of the Monge-Ampere energy functional on the space of Kaehler metrics. It is expected that the study of csck metric is deeply connected to that of Monge-Ampere equations. I discovered a dynamical system on the space of Kahler metrics which discretizes the modified KRF (the evolution equation obtained by replacing -Ric(ω)+ω in the RHS of KRF by -Ric(ω)+HRic(ω), where H means the harmonic part). This dynamical system consists of iteration of the following procedure. First we solve a Poisson equation for u so that the trace of Ric(ω)+ddc u becomes constant. Next we solve the Monge-Ampere equation Ric(ω(φ))=Ric(ω)+ddc u for φ to get a Kaehler metric whose Ricci form coincides with Ric(ω)+ddc u. This procedure constitutes the basic step of out dynamical system. The iteration of this procedure is our dynaical system. This dynakical system fixes cdcK metric.
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