Monge-Ampère equations on quasi-projective varieties
Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016
Location: MSRI: Simons Auditorium
differential geometry
Manifolds
geodesic flow
curvature
compact Kahler manifold
Divisors
Monge-Ampere equation
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C44 - Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C26 - Hyper-Kähler and quaternionic Kähler geometry, 'special' geometry
14415
We consider X a compact Kaehler manifold and D a divisor in X. We study the regularity of solutions of degenerate complex Monge-Ampère equations where the right hand-side is smooth just outside D, establishing uniform a priori estimates which generalize both Yau's and Kolodziej's celebrated estimates.
This is a joint work with Hoang-Chinh Lu.
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14415
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