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Relevant bibliographies by topics / Lagrangian embeddings

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Journal articles

Academic literature on the topic 'Lagrangian embeddings'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Lagrangian embeddings"

1

Yoshiyasu, Toru. "On Lagrangian embeddings into the complex projective spaces." International Journal of Mathematics 27, no. 05 (2016): 1650044. http://dx.doi.org/10.1142/s0129167x16500440.

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We prove that for any closed orientable connected [Formula: see text]-manifold [Formula: see text] and any Lagrangian immersion of the connected sum [Formula: see text] either into the complex projective [Formula: see text]-space [Formula: see text] or into the product [Formula: see text] of the complex projective line and the complex projective plane, there exists a Lagrangian embedding which is homotopic to the initial Lagrangian immersion. To prove this, we show that Eliashberg–Murphy’s [Formula: see text]-principle for Lagrangian embeddings with a concave Legendrian boundary and Ekholm–Eliashberg–Murphy–Smith’s [Formula: see text]-principle for self-transverse Lagrangian immersions with the minimal or near-minimal number of double points hold for six-dimensional simply connected compact symplectic manifolds.

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2

Müller, Stefan. "C0-characterization of symplectic and contact embeddings and Lagrangian rigidity." International Journal of Mathematics 30, no. 09 (2019): 1950035. http://dx.doi.org/10.1142/s0129167x19500356.

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We present a novel [Formula: see text]-characterization of symplectic embeddings and diffeomorphisms in terms of Lagrangian embeddings. Our approach is based on the shape invariant, which was discovered by Sikorav and Eliashberg, intersection theory and the displacement energy of Lagrangian submanifolds, and the fact that non-Lagrangian submanifolds can be displaced immediately. This characterization gives rise to a new proof of [Formula: see text]-rigidity of symplectic embeddings and diffeomorphisms. The various manifestations of Lagrangian rigidity that are used in our arguments come from [Formula: see text]-holomorphic curve methods. An advantage of our techniques is that they can be adapted to a [Formula: see text]-characterization of contact embeddings and diffeomorphisms in terms of coisotropic (or pre-Lagrangian) embeddings, which in turn leads to a proof of [Formula: see text]-rigidity of contact embeddings and diffeomorphisms. We give a detailed treatment of the shape invariants of symplectic and contact manifolds, and demonstrate that shape is often a natural language in symplectic and contact topology. We consider homeomorphisms that preserve shape, and propose a hierarchy of notions of Lagrangian topological submanifold. Moreover, we discuss shape-related necessary and sufficient conditions for symplectic and contact embeddings, and define a symplectic capacity from the shape.

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3

Bykov, Dmitri. "Haldane limits via Lagrangian embeddings." Nuclear Physics B 855, no. 1 (2012): 100–127. http://dx.doi.org/10.1016/j.nuclphysb.2011.10.005.

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4

Biran, P. "Lagrangian barriers and symplectic embeddings." Geometric and Functional Analysis 11, no. 3 (2001): 407–64. http://dx.doi.org/10.1007/pl00001678.

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5

Hofer, Helmut. "Lagrangian embeddings and critical point theory." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2, no. 6 (1985): 407–62. http://dx.doi.org/10.1016/s0294-1449(16)30394-8.

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6

Cieliebak, K., and K. Mohnke. "Punctured holomorphic curves and Lagrangian embeddings." Inventiones mathematicae 212, no. 1 (2017): 213–95. http://dx.doi.org/10.1007/s00222-017-0767-8.

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7

Han, Qing, and Guofang Wang. "Hessian surfaces and local Lagrangian embeddings." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 3 (2018): 675–85. http://dx.doi.org/10.1016/j.anihpc.2017.07.003.

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8

KASUYA, NAOHIKO, and TORU YOSHIYASU. "ON LAGRANGIAN EMBEDDINGS OF PARALLELIZABLE MANIFOLDS." International Journal of Mathematics 24, no. 09 (2013): 1350073. http://dx.doi.org/10.1142/s0129167x13500730.

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We prove that for any closed parallelizable n-manifold Mn, if the dimension n ≠ 7, or if n = 7 and the Kervaire semi-characteristic χ½(M7) is zero, then Mn can be embedded in the Euclidean space ℝ2n with a certain symplectic structure as a Lagrangian submanifold. By the results of Gromov and Fukaya, our result gives rise to symplectic structures of ℝ2n(n ≥ 3) which are not conformally equivalent to open domains in standard ones.

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9

Ramos, Vinicius Gripp Barros. "Symplectic embeddings and the Lagrangian bidisk." Duke Mathematical Journal 166, no. 9 (2017): 1703–38. http://dx.doi.org/10.1215/00127094-0000011x.

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10

Biran, Paul, and Kai Cieliebak. "Lagrangian embeddings into subcritical Stein manifolds." Israel Journal of Mathematics 127, no. 1 (2002): 221–44. http://dx.doi.org/10.1007/bf02784532.

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