On regularization of plurisubharmonic functions on manifolds
Zbigniew Błocki,Sławomir Kołodziej +1 more
- Vol. 135, Iss: 7, pp 2089-2093
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In this paper, the question of when a γ-plurisubharmonic function on a complex manifold, where γ is a fixed (1, 1)-form, can be approximated by a decreasing sequence of smooth 7-PLURISUBharmonic functions was studied.Abstract:
We study the question of when a γ-plurisubharmonic function on a complex manifold, where γ is a fixed (1, 1)-form, can be approximated by a decreasing sequence of smooth 7-plurisubharmonic functions. We show in particular that it is always possible in the compact Kahler case.read more
Citations
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Monge-Ampère equations in big cohomology classes
TL;DR: In this paper, the authors define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kahler manifold X and show that the solution has minimal singularities in the sense of Demailly if μ has L 1+e-density with respect to Lebesgue measure.
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Singular Kähler-Einstein metrics
TL;DR: In this paper, the degenerate complex Monge-Ampere equations of the form $(\omega+dd^c\f)^n = e^{t \f}\mu$ were studied.
Journal ArticleDOI
A variational approach to complex Monge-Ampère equations
TL;DR: In this article, the degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kahler manifold can be solved using a variational method, without relying on Yau's theorem.
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Monge-Amp\`ere equations in big cohomology classes
TL;DR: In this article, the authors define non-pluripolar products of closed positive currents on a compact Kaehler manifold and show that a positive nonplur bipolar measure can be written in a unique way as the top degree self-intersection of a closed positive current in given big cohomology class.
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Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
TL;DR: In this paper, the existence and uniqueness of the normalized Kahler-Ricci flow on non-singular Fano manifolds with log terminal singularities has been proved.
References
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Journal ArticleDOI
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
TL;DR: In this paper, the Ricci form of some Kahler metric is shown to be closed and its cohomology class must represent the first Chern class of M. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation.
Journal ArticleDOI
A new capacity for plurisubharmonic functions
Regularization of closed positive currents and Intersection Theory
TL;DR: In this article, it was shown that the weak limit of a sequence of smooth closed real (1, 1)-currents with small negative part can be bounded in terms of the Lelong numbers of T, once a lower bound for the curvature of the tangent bundle TX is known.
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Intrinsic capacities on compact Kähler manifolds
Vincent Guedj,Ahmed Zeriahi +1 more
TL;DR: In this article, the authors studied fine properties of quasiplurisubharmonic functions on compact Kahler manifolds and showed that locally pluripolar sets are globally quasi-pluripolar.
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Numerical characterization of the Kahler cone of a compact Kahler manifold
Jean-Pierre Demailly,Mihai Paun +1 more
TL;DR: In this paper, it was shown that the Kahler cone depends only on the intersection form of the cohomology ring, the Hodge structure and the homology classes of analytic cycles.