Homotopy Invariants for Solutions to Symplectic Monge Ampere Equations
نویسندگان
چکیده
منابع مشابه
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 ...
متن کاملThe 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...
متن کاملA 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...
متن کاملOn 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...
متن کاملEntire Invariant Solutions to Monge-ampère Equations
We prove existence and regularity of entire solutions to MongeAmpère equations invariant under an irreducible action of a compact Lie group. We consider Monge-Ampère equations of the form f(∇φ) detDijφ = g(x) (0.1) where f and g are nonnegative measurable functions on R. We recall first the concept of a weak solution of (0.1). Let φ be a convex function. Then ∇φ is a well-defined multi-valued m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1993
ISSN: 0022-0396
DOI: 10.1006/jdeq.1993.1109