Results 11  20
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98
RANDOM HOLOMORPHIC ITERATIONS AND DEGENERATE SUBDOMAINS OF THE UNIT DISK
, 2005
"... Abstract. Given a random sequence of holomorphic maps f1, f2, f3,... of the unit disk ∆ to a subdomain X, we consider the compositions Fn = f1 ◦ f2 ◦... fn−1 ◦ fn. The sequence {Fn} is called the iterated function system coming from the sequence f1, f2, f3,.... We prove that a sufficient condition o ..."
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Cited by 6 (4 self)
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Abstract. Given a random sequence of holomorphic maps f1, f2, f3,... of the unit disk ∆ to a subdomain X, we consider the compositions Fn = f1 ◦ f2 ◦... fn−1 ◦ fn. The sequence {Fn} is called the iterated function system coming from the sequence f1, f2, f3,.... We prove that a sufficient condition
Jholomorphic disks and Lagrangian Squeezing, math.SG/0309205
 10 Mohnke, K.: Holomorphic Disks and the Chord Conjecture, Annals of Math
, 2001
"... In this article, we define an invariant for Lagrangian submanifold and prove that if the Lagrangian submanifold contained in the ball of radius r, then the invariant is less than 4πr 2. This modifies Gromov’s Lagrangian embedding theorem. Keywords Symplectic geometry, Jholomorphic curves, Chord. 20 ..."
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Cited by 1 (1 self)
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In this article, we define an invariant for Lagrangian submanifold and prove that if the Lagrangian submanifold contained in the ball of radius r, then the invariant is less than 4πr 2. This modifies Gromov’s Lagrangian embedding theorem. Keywords Symplectic geometry, Jholomorphic curves, Chord
DISK ENUMERATION ON THE QUINTIC 3FOLD
, 2006
"... Abstract. Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to sati ..."
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Cited by 36 (4 self)
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Abstract. Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown
RIGIDITY OF HOLOMORPHIC GENERATORS AND
"... ABSTRACT. In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point of the open unit disk . Namely, if f 2 Hol(; C) is the generator of a oneparameter continuous semigroup fFtgt0, we show that the equality f(z) = o jz j3 when z! ..."
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ABSTRACT. In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point of the open unit disk . Namely, if f 2 Hol(; C) is the generator of a oneparameter continuous semigroup fFtgt0, we show that the equality f(z) = o jz j3 when z
Spectral Invariance for . . .
, 2001
"... We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is ..."
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is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of noncompact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using semiideals, one
ON THE COUNTING OF HOLOMORPHIC DISCS IN TORIC FANO MANIFOLDS
, 2006
"... Abstract. We first compute threepoint open GromovWitten numbers of Lagrangian torus fibers in toric Fano manifolds and show that they depend on the choice of three points, hence they are not invariants. Then, we find a sufficient (but restrictive) condition on a family of chains on a Lagrangian su ..."
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Cited by 4 (1 self)
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Abstract. We first compute threepoint open GromovWitten numbers of Lagrangian torus fibers in toric Fano manifolds and show that they depend on the choice of three points, hence they are not invariants. Then, we find a sufficient (but restrictive) condition on a family of chains on a Lagrangian
Higher cohomology triples and holomorphic extensions, preprint
, 1995
"... Abstract. We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a HitchinKobayashi correspondence between a certain deformation of the HermitianEinstein ..."
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Cited by 10 (1 self)
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Einstein equations and our definition of stability for an extension. Let E − → X be a fixed smooth bundle over a Kähler manifold. There are three natural moduli spaces associated to E; one algebraic, one complex analytic, and one symplectic. The first is the moduli space of slope stable holomorphic structures on E
EMBEDDED CURVES AND GROMOVWITTEN INVARIANTS OF THREEFOLDS
, 2004
"... Abstract. Associated with a prime homology class β ∈ P2(X, Z) (i.e. β = pα and α ∈ H2(X, Z) imply p = 1 or p is an odd prime) on a symplectic threemanifold with vanishing first Chern class, we count the embedded perturbed pseudoholomorphic curves in X of a fixed genus g to obtain certain integer v ..."
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Cited by 1 (0 self)
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Abstract. Associated with a prime homology class β ∈ P2(X, Z) (i.e. β = pα and α ∈ H2(X, Z) imply p = 1 or p is an odd prime) on a symplectic threemanifold with vanishing first Chern class, we count the embedded perturbed pseudoholomorphic curves in X of a fixed genus g to obtain certain integer
Rozansky–Wittentype invariants from symplectic Lie pairs
, 2014
"... We introduce symplectic structures on Lie pairs of (real or complex) algebroids as studied by Chen, Stiénon, and the second author in [4], encompassing homogeneous symplectic spaces, symplectic manifolds with a gaction, and holomorphic symplectic manifolds. We show that to each such symplectic Lie ..."
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Lie pair are associated Rozansky–Wittentype invariants of threemanifolds and knots, given respectively by weight systems on trivalent and chord diagrams. Contents
ALGEBRAS GENERATED BY TWO BOUNDED HOLOMORPHIC FUNCTIONS
, 2002
"... Abstract. We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension (of the closure) of such algebras. The conditions are express ..."
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Cited by 1 (0 self)
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Abstract. We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension (of the closure) of such algebras. The conditions
Results 11  20
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98