# Inner and outer hamiltonian capacities

Bulletin de la Société Mathématique de France (2004)

- Volume: 132, Issue: 4, page 509-541
- ISSN: 0037-9484

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topHermann, David. "Inner and outer hamiltonian capacities." Bulletin de la Société Mathématique de France 132.4 (2004): 509-541. <http://eudml.org/doc/272349>.

@article{Hermann2004,

abstract = {The aim of this paper is to compare two symplectic capacities in $\mathbb \{C\}^n$ 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 is nonzero.},

author = {Hermann, David},

journal = {Bulletin de la Société Mathématique de France},

keywords = {symplectic capacities; lagrangian submanifolds},

language = {eng},

number = {4},

pages = {509-541},

publisher = {Société mathématique de France},

title = {Inner and outer hamiltonian capacities},

url = {http://eudml.org/doc/272349},

volume = {132},

year = {2004},

}

TY - JOUR

AU - Hermann, David

TI - Inner and outer hamiltonian capacities

JO - Bulletin de la Société Mathématique de France

PY - 2004

PB - Société mathématique de France

VL - 132

IS - 4

SP - 509

EP - 541

AB - The aim of this paper is to compare two symplectic capacities in $\mathbb {C}^n$ 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 is nonzero.

LA - eng

KW - symplectic capacities; lagrangian submanifolds

UR - http://eudml.org/doc/272349

ER -

## References

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- [12] L. Traynor – « Symplectic homology via generating functions », Geom. Funct. Anal. 4 (1994), no. 6, p. 718–748. Zbl0822.58020MR1302337
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