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math.AP2019★ 2 cited
Parabolic complex Monge-Ampere equations on compact Kahler manifolds
Sebastien Picard, Xiangwen Zhang
We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the He…
math.AP2016★ 4 cited
Concavity of the Lagrangian Phase Operator and Applications
Tristan C. Collins, Sebastien Picard, Xuan Wu
We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if is a compact domain in o…
math.AP2013
A Priori Estimates of the Degenerate Monge-Ampere Equation on Kahler Manifolds of Nonnegative Bisectional Curvature
Sebastien Picard
The regularity theory of the degenerate complex Monge-Ampère equation is studied. The equation is considered on a closed compact Kähler manifold with nonnegative orthogonal…