Examples of almost-holomorphic and totally real laminations in complex surfaces

Bertrand Deroin

doi:10.1016/j.top.2005.09.001

Examples of almost-holomorphic and totally real laminations in complex surfaces

Bertrand Deroin

Max Planck Institute

Research output: Contribution to journal › Article › peer-review

Abstract

We show that there exists a Lipschitz almost-complex structure J on C P², arbitrarily close to the standard one, and a compact lamination by J-holomorphic curves satisfying the following properties: it is minimal, it has hyperbolic holonomy and it is transversally Lipschitz. Its transverse Hausdorff dimension can be any number δ in an interval ( 0, δ_max ) where δ_max = 1.6309 ... . We also show that there is a compact lamination by totally real surfaces in C² with the same properties, unless the transverse dimension can be any number 0 < δ < 1. Our laminations are transversally totally disconnected.

Original language	English
Pages (from-to)	495-512
Number of pages	18
Journal	Topology
Volume	45
Issue number	3
DOIs	https://doi.org/10.1016/j.top.2005.09.001
Publication status	Published - 1 May 2006
Externally published	Yes

Keywords

Branched surfaces
Holomorphic curves
Solenoid
Symplectic surfaces
Totally real surfaces

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10.1016/j.top.2005.09.001

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AB - We show that there exists a Lipschitz almost-complex structure J on C P2, arbitrarily close to the standard one, and a compact lamination by J-holomorphic curves satisfying the following properties: it is minimal, it has hyperbolic holonomy and it is transversally Lipschitz. Its transverse Hausdorff dimension can be any number δ in an interval ( 0, δmax ) where δmax = 1.6309 ... . We also show that there is a compact lamination by totally real surfaces in C2 with the same properties, unless the transverse dimension can be any number 0 < δ < 1. Our laminations are transversally totally disconnected.

KW - Branched surfaces

KW - Holomorphic curves

KW - Solenoid

KW - Symplectic surfaces

KW - Totally real surfaces

UR - https://www.scopus.com/pages/publications/33645928770

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VL - 45

SP - 495

EP - 512

JO - Topology

JF - Topology

IS - 3

ER -

Examples of almost-holomorphic and totally real laminations in complex surfaces

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Keywords

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