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MASLOV INDEX OF HOLOMORPHIC TRIANGLES
, 2006
"... Abstract. In this short article, we shall try to find an explicit formula for Maslov index of triangles joining intersections points of three halfdimensional tori in the symmetric product of a surface. The method will also yield a formula for the intersection number of such a triangle with the flat ..."
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Cited by 8 (1 self)
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Abstract. In this short article, we shall try to find an explicit formula for Maslov index of triangles joining intersections points of three halfdimensional tori in the symmetric product of a surface. The method will also yield a formula for the intersection number of such a triangle
Holomorphic triangle invariants and the topology of symplectic fourmanifolds
 Duke Math. J
"... This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth fourmanifolds constructed using holomorphic triangles introduced in [20]. Specifically, we establish a nonvanishing result for the invariants of symplectic fourmanifolds, which leads to new ..."
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Cited by 46 (5 self)
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This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth fourmanifolds constructed using holomorphic triangles introduced in [20]. Specifically, we establish a nonvanishing result for the invariants of symplectic fourmanifolds, which leads
Holomorphic triangles and invariants for smooth fourmanifolds
"... Abstract. The aim of this article is to introduce invariants of oriented, smooth, closed fourmanifolds, built using the Floer homology theories defined in [8] and [12]. This fourdimensional theory also endows the corresponding threedimensional theories with additional structure: an absolute gradi ..."
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Cited by 124 (24 self)
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grading of certain of its Floer homology groups. The cornerstone of these constructions is the study of holomorphic disks in the symmetric products of Riemann surfaces. 1.
Admissible, Eudoxus, Geometric Functions of Essentially Holomorphic Triangles and Pascal’s Conjecture
"... Let M ̸ = z be arbitrary. In [21], the main result was the characterization of essentially Lambert categories. We show that J (Λ) ≡ −1. In [21], the authors extended partial, hyperuniversally continuous scalars. It is essential to consider that M may be negative definite. 1 ..."
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Let M ̸ = z be arbitrary. In [21], the main result was the characterization of essentially Lambert categories. We show that J (Λ) ≡ −1. In [21], the authors extended partial, hyperuniversally continuous scalars. It is essential to consider that M may be negative definite. 1
3 PROPER HOLOMORPHIC MAPPINGS BETWEEN COMPLEX ELLIPSOIDS AND GENERALIZED HARTOGS TRIANGLES
"... ar ..."
HOLOMORPHIC INVARIANCE OF STEIN NEIGHBORHOOD BASES
, 2008
"... Abstract. Let Ω be a smooth bounded pseudoconvex domain in Cn. We give several characterizations for the closure of Ω to have a Stein neighborhood basis in the sense that Ω has a defining function ρ such that {z ∈ Cn: ρ(z) < ε} is pseudoconvex for sufficiently small ε> 0. We also show that thi ..."
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that this condition is invariant under proper holomorphic maps that extend smoothly to the boundary. 1. introduction A domain Ω ⊂ Cn is called a domain of holomorphy if there exists a holomorphic function on Ω that cannot be “extended ” past any boundary point. Any domain in C is a domain of holomorphy. However
Rigidity and Flexibility of Triangle Groups in Complex Hyperbolic Geometry
, 1999
"... We show that the Teichmuller space of the triangle groups of type (p; q; 1) in the automorphism group of the two dimensional complex hyperbolic space contains open sets of 0, 1 and 2 real dimensions. In particular we identify the Teichmuller space near embeddings of the modular group preserving a co ..."
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Cited by 10 (3 self)
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We show that the Teichmuller space of the triangle groups of type (p; q; 1) in the automorphism group of the two dimensional complex hyperbolic space contains open sets of 0, 1 and 2 real dimensions. In particular we identify the Teichmuller space near embeddings of the modular group preserving a
Carleson measures for the analytic Besov spaces: The UPPER TRIANGLE CASE
, 2005
"... For a large family of weights ρ in the unit disc and for fixed 1 < q < p < ∞, we give a characterization of those measures µ such that, for all functions f holomorphic in the unit disc, ‖f ‖ L q (µ) ≤ C(µ) (1 − z ..."
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Cited by 34 (14 self)
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For a large family of weights ρ in the unit disc and for fixed 1 < q < p < ∞, we give a characterization of those measures µ such that, for all functions f holomorphic in the unit disc, ‖f ‖ L q (µ) ≤ C(µ) (1 − z
Triangle groups and Jacobians of CM type
"... In the last years, two new tools have been developed for an approach to the question whether a given nonsingular projective algebraic curve over a number field has a Jacobian of CM type. First, such curves can be characterized by the existence of Belyi functions or Grothendieck’s dessins d’enfants ( ..."
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Cited by 1 (1 self)
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], see Theorem 3) and has applications in particular to curves with many automorphisms (Sections 4 and 7). The key in joining both tools is the use of the canonical representation of the automorphism group G of the curve X on the space of holomorphic differentials. The Jacobian of X is isogenous to a
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