A natural equivalence relation on singularities
A natural graded Lie algebra sheaf over Riemann surfaces
A natural localization of Hardy spaces in several complex variables
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in . The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop’s property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
A new characterization of the analytic surfaces in that satisfy the local Phragmén-Lindelöf condition
We prove that an analytic surface in a neighborhood of the origin in satisfies the local Phragmén-Lindelöf condition at the origin if and only if satisfies the following two conditions: (1) is nearly hyperbolic; (2) for each real simple curve in and each , the (algebraic) limit variety satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure -dimensional analytic variety to satisify .
A new class of almost complex structures on tangent bundle of a Riemannian manifold
In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced -tensor on the tangent bundle using these structures and Liouville -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.
A new class of pluripolar sets
Let D be a domain in ℂⁿ. We introduce a class of pluripolar sets in D which is essentially contained in the class of complete pluripolar sets. An application of this new class to the problem of approximation of holomorphic functions is also given.
A new compactification of the moduli space of curves
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. I.
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. II.
A new division formula for complete intersections
We provide a new division formula for holomorphic mappings. It is given in terms of residue currents and has the advantage of being more explicit and simpler to prove than the previously known formulas.
A new example of a compactification of C3.
A new invariant Kähler metric on relatively compact domains in a complex manifold
We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.
A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition
For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition it is shown that for each real simple curve γ and each d ≥ 1 the limit variety satisfies the strong Phragmén-Lindelöf condition (SPL).
A new proof of a theorem of Grauert and Remmert by L2-Methods.
A New Proof of a Theorem of Hörmander and Wermer.
A new proof of desingularization over fields of characteristic zero.
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This is done by showing that desingularization...
A New Proof of the Newlander-Nirenberg Theorem.
A new proof of the Riemann-Poincaré uniformization theorem.
A non-degeneracy property of extremal mappings and iterates of holomorphic self-mappings
A Note Concerning Radó's Theorem.