Filling Real Hypersurfaces by Pseudoholomorphic Discs

Sukhov, Alexandre; Tumanov, Alexander

doi:10.1007/s12220-008-9012-4

“…For these developments see e.g. the survey by Eliashberg [37] on the technique of filling by holomorphic discs, the collection by Audin and Lafontaine [15], and the papers [59,88,89], among others. This line of work also plays an important role in modern topology, in particular in Floer homology.…”

Section: The Riemann-hilbert Problem and Proper Holomorphic Maps Of B...mentioning

confidence: 99%

Null Holomorphic Curves in $$\mathbb{C}^{3}$$ and Applications to the Conformal Calabi-Yau Problem

Alarcón

¹

,

Forstnerič

²

2015

Complex Geometry and Dynamics

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In this paper we survey some recent contributions by the authors [5,6,7] to the theory of null holomorphic curves in the complex Euclidean space C 3 , as well as their applications to null holomorphic curves in the special linear group SL 2 (C), minimal surfaces in the Euclidean space R 3 , and constant mean curvature one surfaces (Bryant surfaces) in the hyperbolic space H 3 . The paper is an expanded version of the lecture given by the second named author at the Abel Symposium 2013 in Trondheim.

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“…The Diederich-Sukhov-Tumanov normalization has been used very efficiently in [10,11] and it is my feeling that it may be helpful in questions related to pluripolarity (but this is only related to work in progress).…”

mentioning

confidence: 99%

Notes on the Diederich-Sukhov-Tumanov normalization for almost complex structures

Rosay

¹

2009

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“…For these developments see e.g. the survey by Eliashberg [37] on the technique of filling by holomorphic discs, the collection by Audin and Lafontaine [15], and the papers [59,88,89], among others. This line of work also plays an important role in modern topology, in particular in Floer homology.…”

Section: The Riemann-hilbert Problem and Proper Holomorphic Maps Of Bmentioning

confidence: 99%

Complex Geometry and Dynamics

Fornæss¹,

Irgens²,

Wold³

2015

Abel Symposia

2

0

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In this paper we survey some recent contributions by the authors [5,6,7] to the theory of null holomorphic curves in the complex Euclidean space C 3 , as well as their applications to null holomorphic curves in the special linear group SL 2 (C), minimal surfaces in the Euclidean space R 3 , and constant mean curvature one surfaces (Bryant surfaces) in the hyperbolic space H 3 . The paper is an expanded version of the lecture given by the second named author at the Abel Symposium 2013 in Trondheim.

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Filling Real Hypersurfaces by Pseudoholomorphic Discs

Abstract: Abstract. We study pseudoholomorphic discs with boundaries attached to a real hypersurface E in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood of E by the discs.MSC: 32H02, 53C15.

Cited by 4 publications

References 14 publications

Null Holomorphic Curves in $$\mathbb{C}^{3}$$ and Applications to the Conformal Calabi-Yau Problem

Null Holomorphic Curves in $$\mathbb{C}^{3}$$ and Applications to the Conformal Calabi-Yau Problem

Notes on the Diederich-Sukhov-Tumanov normalization for almost complex structures

Complex Geometry and Dynamics

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