On definitions of the pluricomplex Green function
We give several definitions of the pluricomplex Green function and show their equivalence.
On pluriharmonic interpolation.
On symmetry of the pluricomplex Green function for ellipsoids
We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
On the equivalence between locally polar and globally polar sets in
On the Legendre and Laplace transformations
On the orthogonal projections onto spaces of pluriharmonic functions and duality
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle is nef, then for any ε >...
Order functions of plurisubharmonic functions
We consider the following problem: find on a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on which is constant outside a polar set is the order function of a plurisubharmonic function.