Nontrivial solutions for the equations of Monge-Ampere type

Degenerate Monge-Ampere Equations over Projective Manifolds

In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is semi-ample and big with certain generalization to more general cases. Two kinds of arguments are applied to study this problem. One is maximum principle type of argument. The ...

The Dirichlet Problem for Degenerate Complex Monge-ampere Equations

The Dirichlet problem for a Monge-Ampère equation corresponding to a nonnegative, possible degenerate cohomology class on a Kähler manifold with boundary is studied. C1,α estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C1,α geodesic rays in the space of Kähler potentials are constructed for each test configurat...

A Priori Limitations for Solutions of Monge-ampere Equations. Ii* By

In this paper we are concerned with the convergence of solutions of elliptic and analytic Monge-Ampère equations. Theorem 1 gives the principal result of this paper. The example on p.^372 indicates the possibility of certain types of singularities which for linear elliptic equations cannot occur. Theorems 2 and 3 give sufficient conditions for the analyticity of the limit function. These condit...

On Degenerated Monge-Ampere Equations over Closed Kähler Manifolds

X (F ωM ) , 2 we have the following: (1) (Apriori estimate) Suppose u is a weak solution in PSHF∗ωM (X) ∩ L(X) of the equation with the normalization supX u = 0, then there is a constant C such that ‖u‖L∞ ≤ C‖f‖Lp where C only depend on F , ω and p; (2) There would always be a bounded solution for this equation; (3) If F is locally birational, then any bounded solution is actually the unique co...

Triple nontrivial radial convex solutions of systems of Monge-Ampère equations