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171
Green functions with singularities along complex subspaces
 INTERNAT. J. MATH
, 2004
"... We study properties of a Green function GA with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u ≤ log ψ+C, where ψ = (ψ1,..., ψm), ψ1,..., ψm are local generators for the ideal sheaf IA of A, a ..."
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Cited by 16 (8 self)
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We study properties of a Green function GA with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u ≤ log ψ+C, where ψ = (ψ1,..., ψm), ψ1,..., ψm are local generators for the ideal sheaf IA of A, and C is a constant depending on the function u and the generators. A motivation for this study is to estimate global bounded functions from the sheaf IA and thus proving a “Schwarz Lemma ” for IA.
An introduction to potential theory in calibrated geometry, Stony Brook Prerprint
, 2006
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The cohomologies of the Iwasawa manifold and of its small deformations
 J. Geom. Anal. Online First
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The Cauchy problem for the homogeneous MongeAmpère equation, I. TOEPLITZ QUANTIZATION
, 2010
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ON COHOMOLOGICAL DECOMPOSITION OF ALMOSTCOMPLEX MANIFOLDS AND DEFORMATIONS
, 909
"... Abstract. While small deformations of Kähler manifolds are Kähler too, we prove that the cohomological property to be C ∞pureandfull is not a stable condition under small deformations. This property, that has been recently introduced and studied by T.J. Li and W. Zhang in [20] and T. Draghici, T ..."
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Cited by 13 (9 self)
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Abstract. While small deformations of Kähler manifolds are Kähler too, we prove that the cohomological property to be C ∞pureandfull is not a stable condition under small deformations. This property, that has been recently introduced and studied by T.J. Li and W. Zhang in [20] and T. Draghici, T.J. Li and W. Zhang in [11, 12], is weaker than the Kähler one and characterizes the almostcomplex structures that induce a decomposition in cohomology. We also study the stability of this property along curves of almostcomplex structures constructed starting from the harmonic representatives in special cohomology classes. 1.
Embeddability of some strongly pseudoconvex CR manifolds
 electronic). MR MR2320650
"... ABSTRACT. We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifold ..."
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Cited by 12 (3 self)
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ABSTRACT. We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.
Quaternionic MongeAmpère equations
 J. Geom. Anal
"... The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic MongeAmpére equations in quaternionic strictly pseudoconvex bounded domains in H n. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started ..."
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Cited by 10 (7 self)
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The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic MongeAmpére equations in quaternionic strictly pseudoconvex bounded domains in H n. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2]. 0 Introduction. This paper is a continuation of author’s previous paper [2]. In [2] we have developed the necessary algebraic technique and we have introduced and studied the class of plurisubharmonic functions of quaternionic variables (this class was independently introduced also by G. Henkin [29]). The main result
Plurisubharmonicity in a general geometric context
, 2008
"... Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagr ..."
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Cited by 10 (6 self)
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Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagrangian plurisubhamonicity and convexity. It also applies in a number of nongeometric situations. Results include: fundamental properties of P+plurisubharmonic functions, plurisubharmonic distributions and regularity, P+convex domains and P+convex boundaries, topological restrictions on and construction of such domains, continuity of upper envelopes, and solutions of the Dirichlet problem for related MongeAmpèretype equations.