Related papers: Moser-Trudinger inequality for the complex Monge-A…
We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.
We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.
We show that the pluripotential Cauchy-Dirichlet problem for the complex Monge-Amp\`ere flow is solvable for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded…
A complex Monge-Amp\`ere equation for differential $(p,p)$-forms is introduced on compact K\"ahler manifolds. For any $1 \leq p < n$, we show the existence of smooth solutions unique up to adding constants. For $p=1$, this corresponds to…
In this article, we study the connection between the fractional Moser-Trudinger inequality and the fractional $\left(\frac{kp}{p-1},p\right)$-Poincar\'e type inequality for any Euclidean domain and discuss the sharpness of this inequality…
We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than -1. Without symmetry assumption, it…
In this paper, we shall study the boundary case for complex Monge-Amp\`ere type equations under certain geometric assumptions.
We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.
In this paper, we introduce a family of real Monge-Amp\`ere functionals and study their variational properties. We prove a Sobolev type inequality for these functionals and use this to study the existence and uniqueness of some associated…
We show that the Moser-Trudinger inequality holds in a conformal disc if and only if the metric is bounded from above by the Hyperbolic metric. We also find a necessary and sufficient condition for the Moser-Trudinger inequality to hold in…
We introduce certain energy functionals to the complex Monge-Ampere equation over a bounded domain with inhomogeneous boundary condition, and use these functionals to show the convergence of the solution to the parabolic Monge-Ampere…
We study a fully nonlinear equation of complex Monge-Ampere type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.
In this note, we establish several results concerning the continuity (or weak convergence) of the complex Monge-Amp\`ere operator on compact Hermitian manifolds. At the end of this note, we find a weak solution of the complex Monge-Amp\`ere…
To a mesh function we associate the natural analogue of the Monge-Ampere measure. The latter is shown to be equivalent to the Monge-Ampere measure of the convex envelope. We prove that the uniform convergence to a bounded convex function of…
We prove that a plurisubharmonic function on a domain in the complex Euclidean space is a locally VMO (Vanishing Mean Oscillation) function if and only if its Lelong number at each point vanishes. We also give a global version of this…
We give a new proof of the almost sharp Moser-Trudinger inequality on compact Riemannian manifolds based on the sharp Moser inequality on Euclidean spaces. In particular we can lower the smoothness requirement of the metric and apply the…
Let $\Omega$ be a bounded, pseudoconvex domain of $\mathbb C^n$ satisfying the "$f$-Property". The $f$-Property is a consequence of the geometric "type" of the boundary; it holds for all pseudoconvex domains of finite type but may also…
A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is nonnegative. We show that the associated Monge-Ampere equation can be solved on any compact…
We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded $\hat{\omega}$-plurisubharmonic solution of an elliptic complex Monge-Amp\`{e}re equation is smooth under an…
We prove that the improved Moser-Trudinger inequality with optimal coefficient $\alpha =1/2$ holds for all functions on $S^2$ with zero moments.