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A Besicovitch cylindrical transformation with Hölder function
Proof of the main conjecture on $g$-areas
1. | Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec |
2. | Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec, Canada |
References:
[1] |
A. Banyaga, Sur la structure du groupe des difféomorphismes qui péservent une forme symplectique, Comment. Math. Helv., 53 (1978), 174-227.
doi: 10.1007/BF02566074. |
[2] |
L. Buhovsky and Y. Ostrover, On the uniqueness of Hofer's geometry, Geom. Funct. Anal., 21 (2011), 1296-1330.
doi: 10.1007/s00039-011-0143-6. |
[3] |
M. Entov, Commutator length of symplectomorphisms, Comment. Math. Helv., 79 (2004), 58-104.
doi: 10.1007/s00014-001-0799-0. |
[4] |
F. Lalonde, A field theory for symplectic fibrations over surfaces, Geom. Topol., 8 (2004), 1189-1226.
doi: 10.2140/gt.2004.8.1189. |
[5] |
F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: Energy and stability of Hamiltonian flows. Part II, Invent. Math., 122 (1995), 35-69.
doi: 10.1007/BF01231437. |
[6] |
F. Lalonde and D. McDuff, Symplectic stuctures on fiber bundles, Topology, 42 (2003), 309-347; Erratum, Topology, 44 (2005), 1301-1303.
doi: 10.1016/S0040-9383(01)00020-9. |
[7] |
F. Lalonde and A. Teleman, The $g$-areas and commutator length, Internat. J. Math., 24 (2013), 1350057, 13 pp.
doi: 10.1142/S0129167X13500572. |
[8] |
D. McDuff, Geometric variants of the Hofer norm, J. Symplectic Geom., 1 (2002), 197-252. |
[9] |
L. Polterovich, The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2001.
doi: 10.1007/978-3-0348-8299-6. |
[10] |
G. M. Tuynman, The Hamiltonian?, in Geometric Methods in Physics. XXXII Workshop, Białowie.za, Poland, June 30-July 6, 2013, Springer International Publishing, Switzerland, 2014, 287-290.
doi: 10.1007/978-3-319-06248-8_25. |
show all references
References:
[1] |
A. Banyaga, Sur la structure du groupe des difféomorphismes qui péservent une forme symplectique, Comment. Math. Helv., 53 (1978), 174-227.
doi: 10.1007/BF02566074. |
[2] |
L. Buhovsky and Y. Ostrover, On the uniqueness of Hofer's geometry, Geom. Funct. Anal., 21 (2011), 1296-1330.
doi: 10.1007/s00039-011-0143-6. |
[3] |
M. Entov, Commutator length of symplectomorphisms, Comment. Math. Helv., 79 (2004), 58-104.
doi: 10.1007/s00014-001-0799-0. |
[4] |
F. Lalonde, A field theory for symplectic fibrations over surfaces, Geom. Topol., 8 (2004), 1189-1226.
doi: 10.2140/gt.2004.8.1189. |
[5] |
F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: Energy and stability of Hamiltonian flows. Part II, Invent. Math., 122 (1995), 35-69.
doi: 10.1007/BF01231437. |
[6] |
F. Lalonde and D. McDuff, Symplectic stuctures on fiber bundles, Topology, 42 (2003), 309-347; Erratum, Topology, 44 (2005), 1301-1303.
doi: 10.1016/S0040-9383(01)00020-9. |
[7] |
F. Lalonde and A. Teleman, The $g$-areas and commutator length, Internat. J. Math., 24 (2013), 1350057, 13 pp.
doi: 10.1142/S0129167X13500572. |
[8] |
D. McDuff, Geometric variants of the Hofer norm, J. Symplectic Geom., 1 (2002), 197-252. |
[9] |
L. Polterovich, The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2001.
doi: 10.1007/978-3-0348-8299-6. |
[10] |
G. M. Tuynman, The Hamiltonian?, in Geometric Methods in Physics. XXXII Workshop, Białowie.za, Poland, June 30-July 6, 2013, Springer International Publishing, Switzerland, 2014, 287-290.
doi: 10.1007/978-3-319-06248-8_25. |
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