Mathematical Physics Seminar
Monday 15.III.2010
Time: 16:00-17:00
Room: 0089
Instytut Matematyki, ul. Łojasiewicza 6, 30-348 Kraków
Zbigniew Błocki
(Uniwersytet Jagielloński, Cracow, Poland)
Donaldson's conjecture on the space of Kähler metrics
Abstract:
We will discuss the space of Kähler metrics introduced by Mabuchi in 1987.
Semmes and Donaldson independently showed that geodesics in this space
satisfy the homogeneous Monge-Ampère equation with boundary condition.
A still open conjecture of Donaldson asserts that any pair of metrics can be
joined by a smooth geodesic. We will present some partial results (the main
progress so far is due to X.X. Chen) and the relation to the problem of
uniqueness of constant scalar curvature metrics.
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