Displaying similar documents to “Submanifolds and the Hofer norm”

Submanifold averaging in Riemannian and symplectic geometry

Marco Zambon (2006)

Journal of the European Mathematical Society

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We give a canonical construction of an “isotropic average” of given C 1 -close isotropic submanifolds of a symplectic manifold. For this purpose we use an improvement (obtained in collaboration with H. Karcher) of Weinstein’s submanifold averaging theorem and apply “Moser’s trick”. We also present an application to Hamiltonian group actions.

On topologically distinct infinite families of exact Lagrangian fillings

Roman Golovko (2022)

Archivum Mathematicum

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In this note we construct examples of closed connected Legendrian submanifolds in high dimensional contact vector space that admit an arbitrary finite number of topologically distinct infinite families of diffeomorphic, but not Hamiltonian isotopic exact Lagrangian fillings.

Inner and outer hamiltonian capacities

David Hermann (2004)

Bulletin de la Société Mathématique de France

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The aim of this paper is to compare two symplectic capacities in ℂ n related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold...