Recent Publications
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Mathematical
2008
1) Polyfolds And A General Fredholm Theory
2) A General Fredholm Theory III: Fredholm Functors
and Polyfolds
(jointly with K. Wysocki and
E. Zehnder)
2007
1) A General Fredholm Theory II:
Implicit Function Theorems
(jointly with K. Wysocki and
E. Zehnder, to appear GAFA)
2) On the Weinstein conjecture in higher dimensions
(jointly
with P. Albers, to appear Com. Math. Helv)
3) Integration Theory on the Zero
Sets of Polyfold Fredholm Sections
(jointly with K. Wysocki and
2006
1) A General Fredholm Theory I: A
Splicing-Based Differential Geometry
(jointly with K. Wysocki and E. Zehnder, JEMS, Volume 9, Issue 4 (2007), 841--876. )
2005
1) Quantitative
Symplectic Geometry
(jointly with K. Cieliebak, J.
Latschev and F. Schlenk,
in:
Dynamics, Ergodic Theory and Geometry, Series: Mathematical
Sciences Research Institute Publications, Edited by Boris Hasselblatt)
2) A General Fredholm Theory
and Applications
In: Current
Developments in Mathematics 2004, International Press, Year Published: 2006
2004
1)The Weinstein
Conjecture for Planar Contact Structures in Dimension Three
(jointly
with C. Abbas and
2003
1) Compactness Results in Symplectic Field
Theory
Posted 11-26-03 This is a revised version of a paper
previously posted here.
Appeared in “Geometry and Topology”
(jointly with F. Bourgeois,
Y. Eliashberg, K. Wysocki and E. Zehnder)
2001
1) Finite
Energy Cylinders with Small Area
(jointly with K. Wysocki and
E. Zehnder, appeared “Dynamical Systems and Ergodic Theory”)
2000
1) Introduction to Symplectic Field Theory
(jointly with Y. Eliashberg
and A. Givental, appeared in GAFA, Special Volume “Vision 2000”)
2) Pseudoholomorphic Curves and Dynamics in Three Dimensions
(appeared in GAFA, Special
Volume “Vision 2000”)
1999
1) Finite Energy Foliations and Hamiltonian Dynamics
(jointly with K. Wysocki and
E. Zehnder, appeared Annals)
2) Holomorphic Curves and Real Three-Dimensional Dynamics
1998
1) Properties of pseudoholomorphic curves in symplectizations III: Fredholm theory
(jointly with K. Wysocki and
E. Zehnder)
2) Dynamics,
Topology and Holomorphic Curves
Proceedings of the ICM
3) Holomorphic
curves and dynamics in dimension three
Park City/IAS institute
lecture notes
4) A characterization of the tight 3-sphere II
(jointly with K. Wysocki and
E. Zehnder) Comm. Pure Appl. Math.
5) Pseudoholomorphic curves and dynamics
(jointly with E. Zehnder)
Proceedings of the "Arnold-Fest".
6) Symplectic geometry from a dynamical systems point of view
Notes for the Colloquium
Lectures at the AMS Annual Meeting in San Antonio.
1997
1) Holomorphic
curves in contact dynamics
(jointly with M. Kriener) to
appear in the proceedings of a conference on the occasion of the 70th birthday
of P. Lax and L. Nirenberg
2) The
dynamics on three-dimensional strictly convex energy surfaces
(jointly with K. Wysocki and
E. Zehnder) to appear in the "Annals of Mathematics"
1996
1) Unknotted
periodic orbits for Reeb flows on the three-sphere
(jointly with K. Wysocki and
E. Zehnder) Topol. Meth. in Nonli. Analysis 7, 219--244, 1996.
2) Properties
of pseudoholomorphic curves in symplectisations I: Asymptotics
(jointly with K. Wysocki and
E. Zehnder) Ann. Inst. Henri Poincare, Analyse Nonlineaire, Vol. 13, No.3,
337-379, 1996
3) Corrections to "Properties of pseudoholomorphic curves in symplectisations I: Asymptotics
(jointly with K. Wysocki and
E. Zehnder) submitted
4) Properties
of pseudoholomorphic curves in symplectisations IV: Asymptotic with
degeneracies
(jointly with K. Wysocki and
E. Zehnder)
5) Applications of symplectic
homology II
(jointly with K. Cieliebak,
A. Floera and K. Wysocki) Math. Zeit. 223, 27-45, 1996
1995
1) A characterization of the tight 3-sphere I
(jointly with K. Wysocki and
E. Zehnder) Duke Mathematical Journal, Vol. 81, No. 1 , 1995.
2) Correction
to "A characterization of the tight 3-sphere I"
(jointly with K. Wysocki and
E. Zehnder) appeared in the "Duke Mathematical Journal"
3) Lagrangian intersections in contact geometry
(jointly with Y. Eliashberg
and D. Salamon) Geometric and Functional Analysis, Vol.5 No. 2, 244--269, 1995
4) Transversality results in the elliptic Morse theory of the action functional
(jointly with A. Floer and D.
Salamon) Duke Mathematical Journal, Vol. 80 No. 1 , 251-292, 1995.
5) Symplectic homology II: A
General Construction
(jointly with K. Cieliebak
and A. Floer) Math. Zeit. 218, 103-122, 1995
6) Floer homology and Novikov
rings
(jointly with D. Salamon) The
Floer Memorial Volume, Progress in Math. Vol. 133, Birkhaeuser
7) Properties of
pseudoholomorphic curves in symplectisations II: Embedding controls and
algebraic invariants
(jointly with K. Wysocki and E.
Zehnder) Geometric and Functional\ Analysis, Vol. 5 No.2 , 270--328,
8) The Floer Memorial Volume
(jointly with C. Taubes, A.
Weinstein and E. Zehnder) Progress in Mathematics Vol. 133, Birkhaeuser
1994
1) Applications of symplectic
homology I
(jointly with A. Floer and K.
Wysocki) Math. Zeit. 217, 577-606, 1994
2) Symplectic homology I:
Open sets in C^n
(jointly with A. Floer) Math.
Zeit. 215, 37-88, 1994
3) A Hamiltonian
characterization of the three--ball
(jointly with Y. Eliashberg)
Journal of Differential and Integral Equations, Vol.7 No.5 , 1303-1324, 1994'
4) Symplectic Invariants and
Hamiltonian Dynamics
(jointly with E. Zehnder)
Advanced Texts in Mathematics, Birkhaeuser
1993
1) Pseudoholomorphic curves
in symplectisation with applications to the Weinstein conjecture in dimension
three
Inv. Math. 114, 515-563, 1993
2) Estimates for the energy
of a symplectic map
Comm. Math. Helv. 68, 48-72,
1993
3) An energy--capacity
inequality for the symplectic holonomy of hypersurfaces flat at infinity
(jointly with Y. Eliashberg)
Symplectic Geometry, edited by D. Salamon, London Mathematical Society Lecture
Note Series 192, 95-114, 1993
4) Coherent orientation for
periodic orbit problems in symplectic geometry
(jointly with A. Floer) Math.
Zeit. 212, 13-38, 1993
Non-mathematical
1998
Innovation, Venture Capital, Arbeitsplaetze
(jointly with A. Scheidegger and G. Scheuenstuhl, in German ) Haupt Verlag
visitors since 2/21/99