Lusternik-Schnirelman-theory for lagrangian intersections

 Access to full text

 Full (PDF)

1. [1] R. Abraham and J. Marsden, Foundations of Mechanics, Benjamin, CummingsReading, Mass., 1978. Zbl0393.70001MR515141
2. [2] S. Agmon, A. Douglis and L. Nirenberg, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions I, II, Comm. Pure Appl. Math., Vol. 12, 1959, pp. 623-727 and Vol. 17, 1964, pp. 35- 92. Zbl0093.10401MR162050
3. [3] V.I. Arnold, Sur une propriété topologique des applications canoniques de la mécanique classique, C.R. Acad. Sci. Paris, T. 261, 1965, pp. 3719-3722. Zbl0134.42305MR193645
4. [4] N. Aronszajn, A Unique Continuation Theorem for Solutions of Elliptic Partial Differential Equations or Inequalities of the Second Order, J. Math. Pures Appl., (9), Vol. 36, 1957, pp. 235-249. Zbl0084.30402MR92067
5. [5] D. Bennequin, Problèmes elliptiques, surfaces de Riemann et structures symplectiques, Séminaire Bourbaki, 38e année, 1985-1986, No 657. Zbl0644.53031MR880029
6. [6] B. Boos and D.D. Bleeker, Topology and Analysis, Universitext, Springer, 1985. Zbl0551.58031MR771117
7. [7] Y. Borisovich, V. Zvyagin and V. Sapronov, Nonlinear Fredholm maps and Leray Schauder Theory, Russian Math. Survey's, Vol. 32, No. 4, 1977, pp. 1-54. Zbl0383.58002
8. [8] M. Chaperon, Quelques questions de géométrie symplectique, Séminaire Bourbaki 1982/1983, Asterisque, No. 105-106, pp. 231-249. Zbl0525.53049MR728991
9. [9] D.C. Clark, A Variant of Lusternik-Schnirelman-Theory, Indiana University Math. J., Vol. 22, No. 1, 1972, pp. 65-74. Zbl0228.58006MR296777
10. [10] C. Conley and E. Zehnder, The Birkhoff-Lewis Fixed Point Theorem and a Conjecture of V. I. Arnold, Inv. Math., T. 73, 1983, pp. 33-49. Zbl0516.58017MR707347
11. [11] C. Conley and E. Zehnder, Morse Type Index Theory for Flows and Periodic Solutions for Hamiltonian Equations, Comm. Pure and Appl. Math., Vol. 27, 1984, pp. 211-253. Zbl0559.58019MR733717
12. [12] A. Dold, Lectures on Algebraic Topology, Grundlehren der Math. Wissenschaften, Vol. 200, Springer, 2nd edition. Zbl0434.55001
13. [13] H. Eliasson, Geometry of Manifold of Maps, J. Diff. Geometry, 1, 1967, pp. 165-194. Zbl0163.43901
14. [14] D. Freed and V. Uhlenbeck, Instantons and Four-Manifolds, Springer, 1984. Zbl0559.57001MR757358
15. [15] A. Floer, The Unregularized Gradient Flow of the Symplectic Action (preprint). Zbl0633.53058MR948771
16. [16] A. Floer, A Morse Theory for Lagrangian Intersections (preprint). MR876964
17. [17] A. Floer, A Relative Morse Index for the Symplectic Action (preprint). 
18. [18] A. Floer, Proof of the Arnold Conjecture for Surfaces and Generalisations for Certain Kahler Manifolds, Duke Math. J., Vol. 51, 1986, pp. 1-32. Zbl0607.58016MR835793
19. [19] A. Floer, H. Hofer and C. Viterbo, The Weinstein Conjecture in P x Cl (to appear). Zbl0666.58019
20. [20] B. Fortune and A. Weinstein, A Symplectic Fixed Point Theorem for Complex Projective Spaces, Bull. A.M.S., Vol. 12, 1985. Zbl0566.58013MR766969
21. [21] B. Fortune, A Symplectic Fixed Point Theorem for CPn, Inv. Math., Vol. 81 (Fax 1), 1985, pp. 29-46. Zbl0547.58015MR796189
22. [22] M. Gromov, Pseudo-Holomorphic Curves in Symplectic Manifolds, Inv. Math., Vol. 82, 1985, pp. 307-347. Zbl0592.53025
23. [23] M. Gromov and V.A. Rohlin, Imbeddings and Immersions in Riemannian Geometry, Russ. Math. Surveys, Vol. 25, 1970, p. 1-57. Zbl0222.53053MR290390
24. [24] H. Hofer, Lagrangian Embeddings and Critical Point Theory, Ann. I.H.P., Analyse non linéaire, Vol. 2, 1985, pp. 407-462. Zbl0591.58009MR831040
25. [25] H. Hofer and C. Viterbo, The Weinstein Conjecture in Cotangent Bundles and Related Results (to appear). Zbl0697.58044
26. [26] H. Hofer and E. Zehnder, Periodic Solutions on Hypersurfaces and a Result by C. Viterbo, Inv. Math., Vol. 90, 1987, pp. 1-9. Zbl0631.58022MR906578
27. [27] I. Ekeland and H. Hofer, Two Symplectic Fixed Point Theorems (submitted). 
28. [28] L. Hormander, The Analysis of Linear Differential Operators III, Springer, 1985. Zbl0601.35001
29. [29] T. Kato, Perturbation Theory for Linear Operators, Springer, 1976. Zbl0342.47009MR407617
30. [30] W. Klingenberg, Riemannian geometry, de Gruyter studies in Math., Vol. 1, Walter de Gruyter, 1982. Zbl0495.53036MR666697
31. [31] W. Klingenberg, Lectures on Closed Geoderics, Springer, 1978. Zbl0397.58018MR478069
32. [32] N. Kuiper, The Homotopy Type of the Unitary Groups of Hilbert Spaces, Topology, Vol. 3, 1965, pp. 19-30. Zbl0129.38901MR179792
33. [33] F. Laudenbach and J.C. Sikorav, Persistance d'intersections avec la section nulle., Inv. Math., Vol. 82, 1985, pp. 349-357. Zbl0592.58023MR809719
34. [34] D. Mcduff, Examples of Symplectic Structures, Inv. Math., Vol. 89, 1987, pp. 13-36. Zbl0625.53040MR892186
35. [35] R. Palais, Morse Theory on Hilbert Manifolds, Topology, Vol. 2, 1963, pp. 299-340. Zbl0122.10702MR158410
36. [36] R. Palais, Foundations of Global Non-Linear Analysis, Benjamin, 1968. Zbl0164.11102MR248880
37. [37] B. Pansu, Notes sur les pages 316 à 323 de l'article de M. Gromov Pseudoholomorphic Curves in Symplectic Manifolds (preprint). 
38. [38] J. Sacks and V. Uhlenbeck, The Existence of Minimal Immersions of Two Spheres, Ann. Math., Vol. 113, 1981, pp. 1-24. Zbl0462.58014MR604040
39. [39] J.C. Sikorav, Points fixes d'une application symplectique homologue à l'identité, J. Diff. Geom., Vol. 22, 1985, pp. 49-79. Zbl0555.58013MR826424
40. [40] S. Smale, An Infinite-Dimensional Version of Sard's Theorem, Amer. J. Math., Vol. 87, 1965, pp. 861-866. Zbl0143.35301MR185604
41. [41] I.N. Vekua, Generalized Analytic Functions, Pergamon, 1962. Zbl0100.07603
42. [42] C. Viterbo, A Proof of the Weinstein Conjecture in R2 n, Ann. I.H.P., Analyse non linéaire, 1987 (à paraitre). Zbl0631.58013
43. [43] W. Warschawski, On Differentiability at the Boundary in Conformal Mapping, Proc. A.M.S., Vol. 12, 1961, pp. 614-620. Zbl0100.28803MR131524
44. [44] A. Weinstein, Lagrangian Submanifolds and Hamiltonian Systems, Ann. Math., Vol. 98, 1973, pp. 337-410. Zbl0271.58008MR331428
45. [45] A. Weinstein, C0-Perturbation Theorems for Symplectic Fixed Points and Lagrangian Intersections, Séminaire sud-rhodanien de géométrie III, Travaux en cours, Hermann, Paris, 1984, pp. 140-144. Zbl0598.58013
46. [46] A. Weinstein, Symplectic Geometry and the Calculus of Variations, Marston Morse Memorial Lectures, I.A.S., Princeton, 1985 (to appear). 
47. [47] W.L. Wendland, Elliptic Systems in the Plane, Pitman, 1979. Zbl0396.35001MR518816
48. [48] J.G. Wolfson, A. PDE Proof of Gromov's Compactness of Pseudo Holomorphic Curves, preprint, 1986. 
49. [49] E. Zehnder, Some Perspectives in Hamiltonian Systems, preprint. Zbl0582.70017MR853759
50. [50] A. Floer, Cuplength-Estimates on Lagrangian Intersections, preprint. Zbl0683.58017MR990135

1. Kaoru Ono, On Arnold's conjecture for symplectic fixed points
2. Yuli Rudyak, Category weight: new ideas concerning Lusternik-Schnirelmann category