Positive scalar curvature and the Dirac operator on complete riemannian manifolds

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1. [Ag] S. AGMON, Elliptic Boundary Value Problems, Van Nostrand, 1965. Zbl0142.37401MR31 #2504
2. [Al] F. J. ALMGREN, Jr., Existence and regularity almost everywhere to solutions of elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. of Math. 87 (1968), 321-391. Zbl0162.24703MR37 #837
3. [A] M. F. ATIYAH, Elliptic operators, discrete groups and Von Neumann algebras, Astérisque, vol. 32-33, Société Math. de France, 1976, 43-72. Zbl0323.58015MR54 #8741
4. [ABS] M. F. ATIYAH, R. BOTT and A. SHAPIRO, Clifford modules, Topology 3 (Suppl. 1) (1964), 3-38. Zbl0146.19001MR29 #5250
5. [AH] M. F. ATIYAH and F. HIRZEBRUCH, Vector bundles and homogeneous spaces, Proc. Symp. Pure Math. A.M.S. III (1961), 7-38. Zbl0108.17705MR25 #2617
6. [ASI] M. F. ATIYAH and I. SINGER, The index of elliptic operators I, Ann. of Math. 87 (1968), 484-530. Zbl0164.24001MR38 #5243
7. [ASIII] M. F. ATIYAH and I. SINGER, The index of elliptic operators III, Ann. of Math. 87 (1968), 546-604. Zbl0164.24301MR38 #5245
8. [ASV] M. F. ATIYAH and I. SINGER, The index of elliptic operators V, Ann. of Math. 93 (1971), 139-149. Zbl0212.28603MR43 #5555
9. [AS] M. F. ATIYAH and I. SINGER, Index Theory for skew-adjoint Fredholm operators, Publ. Math. I.H.E.S. 37, (1969), 1-26. Zbl0194.55503MR44 #2257
10. [B1] L. BÉRARD BERGERY, La courbure scalaire des variétés riemanniennes, Sém. Bourbaki, exposé n° 556, juin 1980, Springer Lecture Notes 842 (1981), 225-245. Zbl0461.53023MR84f:53032
11. [B2] L. BÉRARD BERGERY, Scalar curvature and isometry group (to appear). 
12. [BT] Yu. D. BURAGO and V. A. TOPONAGOV, On 3-dimensional riemannian spaces with curvature bounded above, Math. Zametki 13 (1973), 881-887. Zbl0277.53025MR49 #11424
13. [BZ] Yu. D. BURAGO and V. A. ZAGALLAR, Geometric Inequalities (in Russian), Leningrad, 1980. Zbl0436.52009
14. [CF] I. CHAVEL and E. FELDMAN, Isoperimetric inequalities on curved surfaces (to appear). Zbl0461.53012
15. [CG] J. CHEEGER and D. GROMOLL, The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom. 6 (1917), 119-128. Zbl0223.53033MR46 #2597
16. [CY] S. Y. CHENG and S. T. YAU, Differential equations on riemannian manifolds and their geometric applications, Comm. Pure and Appl. Math. 28 (1975), 333-354. Zbl0312.53031MR52 #6608
17. [F1] H. FEDERER, Geometric Measure Theory, N.Y., Springer Verlag, 1969. Zbl0176.00801MR41 #1976
18. [F2] H. FEDERER, Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974), 351-407. Zbl0289.49044MR50 #1095
19. [FF] H. FEDERER and W. FLEMING, Normal and integral currents, Ann. of Math. 72 (1960), 458-520. Zbl0187.31301MR23 #A588
20. [Fia] F. FIALA, Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comm. Math. Helv. 13 (1941), 293-346. Zbl0025.23003MR3,301bJFM67.0698.01
21. [F-CS] D. FISCHER-COLBRIE and R. SCHOEN, The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature, Comm. Pure and Appl. Math. 33 (1980), 199-211. Zbl0439.53060MR81i:53044
22. [Fl] W. FLEMING, On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962), 69-90. Zbl0107.31304MR28 #499
23. [Gao] Z. GAO, Thesis, Stony Brook, 1982. 
24. [G] M. GROMOV, Filling riemannian manifolds, J. Diff. Geom. 18 (1983), 1-147. Zbl0515.53037MR85h:53029
25. [GL1] M. GROMOV and H. B. LAWSON, Jr., Spin and scalar curvature in the presence of a fundamental group, Ann. of Math. 111 (1980), 209-230. Zbl0445.53025MR81g:53022
26. [GL2] M. GROMOV and H. B. LAWSON, Jr., The classification of simply-connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434. Zbl0463.53025MR81h:53036
27. [HS] R. HARDT and L. SIMON, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. 110 (1979), 439-486. Zbl0457.49029MR81i:49031
28. [Ha] P. HARTMAN, Geodesic parallel coordinates in the large, Amer. J. Math. 86 (1964), 705-727. Zbl0128.16105MR30 #3435
29. [H] N. HITCHIN, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. Zbl0284.58016MR50 #11332
30. [I] V. K. IONIN, Isoperimetric and certain other inequalities for a manifold of bounded curvature, Sibirski Math. J. 10 (1969), 329-342. Zbl0188.27502MR39 #2098
31. [K] J. KAZDAN, Deforming to positive scalar curvature on complete manifolds, Math. Ann. 261 (1982), 227-234. Zbl0476.53022MR84e:53054
32. [KW] J. KAZDAN and F. WARNER, Prescribing curvatures, Proc. of Symp. in Pure Math. 27 (1975), 309-319. Zbl0313.53017MR52 #15306
33. [KN] S. KOBAYASHI and K. NOMIZU, Foundations of Differential Geometry, N.Y., Interscience, 1963. Zbl0119.37502MR27 #2945
34. [L1] H. B. LAWSON Jr., Minimal Varieties, Proc. of Symp. in Pure Math. 27 (1975), 143-175. Zbl0328.49020MR52 #1496
35. [L2] H. B. LAWSON Jr., The unknottedness of minimal embeddings, Inv. Math. 11 (1970), 183-187. Zbl0205.52002MR44 #4651
36. [LM] H. B. LAWSON Jr. and M. L. MICHELSOHN, Spin Geometry (to appear). 
37. [LY] H. B. LAWSON Jr. and S. T. YAU, Scalar curvature, non-abelian group actions and the degree of symmetry of exotic spheres, Comm. Math. Helv. 49 (1974), 232-244. Zbl0297.57016MR50 #11300
38. [Li] A. LICHNEROWICZ, Spineurs harmoniques, C.r. Acad. Sci. Paris, Sér. A-B, 257 (1963), 7-9. Zbl0136.18401MR27 #6218
39. [Lu] G. LUSZTIG, Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 229-256. Zbl0265.57009MR48 #1250
40. [MSY] W. MEEKS III, L. SIMON and S. T. YAU, Embedded minimal surfaces, exotic spheres and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982), 621-659. Zbl0521.53007
41. [M1] J. MILNOR, On manifolds homemorphic to the 7-sphere, Ann. of Math. (2) 64 (1956), 399-405. Zbl0072.18402MR18,498d
42. [M2] J. MILNOR, Remarks concerning spin manifolds, "Differential Geometry and Combinatorial Topology", Princeton University Press, 1965, 55-62. Zbl0132.19602MR31 #5208
43. [M3] J. MILNOR, Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, 1965. Zbl0136.20402MR37 #2239
44. [M4] J. MILNOR, A Unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7. Zbl0108.36501MR25 #5518
45. [Mi] T. MIYAZAKI, On the existence of positive scalar curvature metrics on non-simply-connected manifolds (to appear). Zbl0541.53034
46. [Mor] C. B. MORREY, Multiple Integrals and the Calculus of Variations, New York, Springer-Verlag, 1966. Zbl0142.38701MR34 #2380
47. [O] R. OSSERMAN, Bonneson-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979), 1-29. Zbl0404.52012MR80h:52013
48. [Sa] T. SAKAI, On a theorem of Burago-Toponogov (to appear). Zbl0512.53042
49. [Sc] H. H. SCHAEFER, Topological Vector Spaces, N.Y., Springer-Verlag, 1971. Zbl0212.14001MR49 #7722
50. [S] R. SCHOEN, A remark on minimal hypercones (to appear). Zbl0488.53043
51. [SY1] R. SCHOEN and S. T. YAU, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds of non-negative scalar curvature, Ann. of Math. 110 (1979), 127-142. Zbl0431.53051MR81k:58029
52. [SY2] R. SCHOEN and S. T. YAU, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. Zbl0423.53032MR80k:53064
53. [SY3] R. SCHOEN and S. T. YAU, Complete three dimensional manifolds with positive Ricci curvature and scalar curvature, in Seminar on differential geometry, Annals of Math. Studies, n° 102, Princeton Univ. Press, 1982, 209-227. Zbl0481.53036MR83k:53060
54. [SY4] R. SCHOEN and S. T. YAU, Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature, Comm. Math. Helv. 39 (1976), 333-341. Zbl0361.53040MR55 #11302
55. [SY5] R. SCHOEN and S. T. YAU (to appear). 
56. [Si] J. SIMONS, Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105. Zbl0181.49702MR38 #1617
57. [T] R. THOM, Quelques propriétés globales des variétés différentiables, Comm. Math. Helv. 28 (1954), 17-86. Zbl0057.15502MR15,890a

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