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

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, J-holomorphic curves, Chord

Abstract. Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold 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

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 gener-ator of a one-parameter continuous semigroup fFtgt0, we show that the equality f(z) = o jz j3 when z

is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using semi-ideals, one

Abstract. We first compute three-point open Gromov-Witten 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

-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

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 three-manifold with vanishing first Chern class, we count the embedded perturbed pseudo-holomorphic curves in X of a fixed genus g to obtain certain integer

Lie pair are associated Rozansky–Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams. Contents

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