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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