Compactness for embedded pseudoholomorphic curves in 3-manifolds

Chris Wendl

Displaying similar documents to “Compactness for embedded pseudoholomorphic curves in 3-manifolds”

Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits.

Valdinoci, Enrico (2000)

Mathematical Physics Electronic Journal [electronic only]

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Exponentially stable manifolds in the neighbourhood of elliptic equilibria

Antonio Giorgilli, Daniele Muraro (2006)

Bollettino dell'Unione Matematica Italiana

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We consider a Hamiltonian system in a neighbourhood of an elliptic equilibrium which is a minimum for the Hamiltonian. With appropriate non-resonance conditions we prove that in the neighbourhood of the equilibrium there exist low dimensional manifolds that are exponentially stable in Nekhoroshev’s sense. This generalizes the theorem of Lyapounov on the existence of periodic orbits. The result may be meaningful for, e.g., the dynamics of non-linear chains of the Fermi-Pasta-Ulam (FPU)...

First steps in stable Hamiltonian topology

Kai Cieliebak, Evgeny Volkov (2015)

Journal of the European Mathematical Society

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In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on $S^{3}$ is homotopic to a stable Hamiltonian structure which cannot be embedded in $ℝ^{4}$ . Moreover, we derive a structure theorem...

On the Stable Reduction of Pencils of Curves.

Gang Xiao (1990)

Mathematische Zeitschrift

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Linear systems over ℙ¹×ℙ¹ with base points of multiplicity bounded by three

Tomasz Lenarcik (2011)

Annales Polonici Mathematici

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We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general position. As an application, we obtain a classification of special linear systems on ℙ¹×ℙ¹ with multiplicities not exceeding 3.