Partial pluricomplex energy and integrability exponents of plurisubharmonic functions
By Per Åhag, U. Cegrell, S. Kołodziej, Hoàng Hiệp Phạm, Ahmed Zeriahi. 2008
57 citations recorded by the source corpus.
We first prove a quantitative estimate of the volume of the sublevel sets of a plurisubharmonic function in a hyperconvex domain with boundary values 0 (in a quite general sense) in terms of its Monge–Ampere mass in the domain. Then we deduce a sharp sufficient condition on the Monge–Ampere mass of such a plurisubharmonic function φ for exp(−2φ) to be globally integrable as well as locally integrable.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/52928af90b6b63f952afa6e3a0569c55bc3dfc14
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds (2013, background): “sing test functions and approximation argument as in the proof in [1, Theorem 3.1]. Indeed, if is smooth, we can choose a negative test function 2E 0(B 1(0)) \C(B 1(0)) with zero boundary values (see [1] for the precise denition of E 0(B 1(0))) and calculate: Z B 1(0) I( p 1@@ ) = Z B 1(0) Z X t M(”