64 citations · 212 across the 30 of their papers we have counts for
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Smooth Approximation of Plurisubharmonic Functions on Almost Complex Manifolds
F. Reese Harvey, H. Blaine Lawson, Szymon Pliś
This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoco…
Potential Theory on Almost Complex Manifolds
F. Reese Harvey, H. Blaine Lawson
Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined c…
The Projective Hull of Certain Curves in C^2
F. Reese Harvey, H. Blaine Lawson, John Wermer
The projective hull X^ of a subset X in complex projective space P^n is an analogue of the classical polynomial hull of a set in C^n. If X is contained in an affine chart C^n on P^…
Remarks on the Alexander-Wermer Theorem for Curves
F. Reese Harvey, H. Blaine Lawson
We give a new proof of the Alexander-Wermer Theorem that characterizes the oriented curves in C^n which bound positive holomorphic chains, in terms of the linking numbers of the cu…
Boundaries of Positive Holomorphic Chains and the Relative Hodge Question
F. Reese Harvey, H. Blaine Lawson
We characterize the boundaries of positive holomorphic chains (with both compact and non-compact support) in an arbitrary complex manifold. We then consider a compact oriented real…
Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part II
F. Reese Harvey, H. Blaine Lawson
In Part I of this paper we introduced the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space…
Plurisubharmonic Functions in Calibrated Geometries
F. Reese Harvey, H. Blaine Lawson
In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from compl…
Boundaries of Varieties in Projective Manifolds
F. Reese Harvey, H. Blaine Lawson
We give a characterization of the boundaries of holomorphic chains in complex projective space in terms of certain non-linear moment conditions. This extends previous work of the a…
Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I
F. Reese Harvey, H. Blaine Lawson
We introduce the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space P^n with an algebraic su…
Projective Hulls and the Projective Gelfand Transformation
F. Reese Harvey, H. Blaine Lawson
We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a…
Addendum to Theorem 10.4 in "Boundaries of Analytic Varieties"
F. Reese Harvey, H. Blaine Lawson
The main result of [HL] (Annals of Math. 102 (1975), 223--290) gives a characterization of the boundaries of complex subvarieties in C^n. An application of this result concerning p…