On regularization of plurisubharmonic functions on manifolds

By Zbigniew Blocki, S. Kołodziej. 2007

196 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/408ca71381cbd7f48f34d9202050d903d971cf06

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Monge–Ampère equations in big cohomology classes (2008, background): “By Demailly’s approximation theorem [16] we can find decreasing sequences of smooth functions φ i decreasing towards φi, as k!∞, and such that ddφ (k) i >−ω for some fixed large enough Kähler form ω (see also [9]).”
A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry (2013, methodology): “This is basically the main result in [9], and for the convenie nc of the reader we translate to the language of γ-plurisubharmonic functions used in that paper.”
A thermodynamical formalism for Monge–Ampère equations, Moser–Trudinger inequalities and Kähler–Einstein metrics (2010, background): “See also [17] for a simple proof of the last statement in the following proposition.”
Geometric pluripotential theory on Kähler manifolds (2019, methodology): “Here we will follow closely the arguments of Blocki–Kolodziej [23].”
A numerical criterion for generalised Monge-Ampère equations on projective manifolds (2020, methodology): “The basic idea is to cover the manifolds with balls of a small but definite size on which the current can be written as the √ −1∂∂̄ of some potentials, and then to glue these potentials to ψU using the modification of the Richberg technique [14] due to Blocki-Kolodziej [2], and its improvement (to a”
On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds (2010, background): “In fact these generalizations are direct consequence of results from [3] and [4].”
Nakai-Moishezon criterions for complex Hessian equations (2020, methodology): “ ε<<λ −1δ 0 suﬃciently small.29 6. Gluing argument In this section, we will follow the idea of Chen [6] for gluing the local potentials by induction assumption and the trick of Blocki-Kolodziej [1]. The main diﬀerence of our argument from [6] is that we do not assume the pluriclosed set of the”