@article{PMIHES_1983__58__83_0, author = {Gromov, Mikhael and Lawson, H. Blaine}, title = {Positive scalar curvature and the Dirac operator on complete riemannian manifolds}, journal = {Publications Math\'ematiques de l'IH\'ES}, volume = {58}, year = {1983}, pages = {83-196}, mrnumber = {85g:58082}, zbl = {0538.53047}, language = {en}, url = {http://dml.mathdoc.fr/item/PMIHES_1983__58__83_0} }
Gromov, Mikhael; Lawson, H. Blaine. Positive scalar curvature and the Dirac operator on complete riemannian manifolds. Publications Mathématiques de l'IHÉS, Tome 58 (1983) pp. 83-196. http://gdmltest.u-ga.fr/item/PMIHES_1983__58__83_0/
[Ag] Elliptic Boundary Value Problems, Van Nostrand, 1965. | MR 31 #2504 | Zbl 0142.37401
,[Al] 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. | MR 37 #837 | Zbl 0162.24703
, ,[A] Elliptic operators, discrete groups and Von Neumann algebras, Astérisque, vol. 32-33, Société Math. de France, 1976, 43-72. | MR 54 #8741 | Zbl 0323.58015
,[ABS] Clifford modules, Topology 3 (Suppl. 1) (1964), 3-38. | MR 29 #5250 | Zbl 0146.19001
, and ,[AH] Vector bundles and homogeneous spaces, Proc. Symp. Pure Math. A.M.S. III (1961), 7-38. | MR 25 #2617 | Zbl 0108.17705
and ,[ASI] The index of elliptic operators I, Ann. of Math. 87 (1968), 484-530. | MR 38 #5243 | Zbl 0164.24001
and ,[ASIII] The index of elliptic operators III, Ann. of Math. 87 (1968), 546-604. | MR 38 #5245 | Zbl 0164.24301
and ,[ASV] The index of elliptic operators V, Ann. of Math. 93 (1971), 139-149. | MR 43 #5555 | Zbl 0212.28603
and ,[AS] Index Theory for skew-adjoint Fredholm operators, Publ. Math. I.H.E.S. 37, (1969), 1-26. | Numdam | MR 44 #2257 | Zbl 0194.55503
and ,[B1] La courbure scalaire des variétés riemanniennes, Sém. Bourbaki, exposé n° 556, juin 1980, Springer Lecture Notes 842 (1981), 225-245. | Numdam | MR 84f:53032 | Zbl 0461.53023
,[B2] Scalar curvature and isometry group (to appear).
,[BT] On 3-dimensional riemannian spaces with curvature bounded above, Math. Zametki 13 (1973), 881-887. | MR 49 #11424 | Zbl 0277.53025
and ,[BZ] Geometric Inequalities (in Russian), Leningrad, 1980. | Zbl 0436.52009
and ,[CF] Isoperimetric inequalities on curved surfaces (to appear). | Zbl 0461.53012
and ,[CG] The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom. 6 (1917), 119-128. | MR 46 #2597 | Zbl 0223.53033
and ,[CY] Differential equations on riemannian manifolds and their geometric applications, Comm. Pure and Appl. Math. 28 (1975), 333-354. | MR 52 #6608 | Zbl 0312.53031
and ,[F1] Geometric Measure Theory, N.Y., Springer Verlag, 1969. | MR 41 #1976 | Zbl 0176.00801
,[F2] Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974), 351-407. | MR 50 #1095 | Zbl 0289.49044
,[FF] Normal and integral currents, Ann. of Math. 72 (1960), 458-520. | MR 23 #A588 | Zbl 0187.31301
and ,[Fia] Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comm. Math. Helv. 13 (1941), 293-346. | JFM 67.0698.01 | MR 3,301b | Zbl 0025.23003
,[F-CS] The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature, Comm. Pure and Appl. Math. 33 (1980), 199-211. | MR 81i:53044 | Zbl 0439.53060
and ,[Fl] On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962), 69-90. | MR 28 #499 | Zbl 0107.31304
,[Gao] Thesis, Stony Brook, 1982.
,[G] Filling riemannian manifolds, J. Diff. Geom. 18 (1983), 1-147. | MR 85h:53029 | Zbl 0515.53037
,[GL1] Spin and scalar curvature in the presence of a fundamental group, Ann. of Math. 111 (1980), 209-230. | MR 81g:53022 | Zbl 0445.53025
and ,[GL2] The classification of simply-connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434. | MR 81h:53036 | Zbl 0463.53025
and ,[HS] Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. 110 (1979), 439-486. | MR 81i:49031 | Zbl 0457.49029
and ,[Ha] Geodesic parallel coordinates in the large, Amer. J. Math. 86 (1964), 705-727. | MR 30 #3435 | Zbl 0128.16105
,[H] Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | MR 50 #11332 | Zbl 0284.58016
,[I] Isoperimetric and certain other inequalities for a manifold of bounded curvature, Sibirski Math. J. 10 (1969), 329-342. | MR 39 #2098 | Zbl 0188.27502
,[K] Deforming to positive scalar curvature on complete manifolds, Math. Ann. 261 (1982), 227-234. | MR 84e:53054 | Zbl 0476.53022
,[KW] Prescribing curvatures, Proc. of Symp. in Pure Math. 27 (1975), 309-319. | MR 52 #15306 | Zbl 0313.53017
and ,[KN] Foundations of Differential Geometry, N.Y., Interscience, 1963. | MR 27 #2945 | Zbl 0119.37502
and ,[L1] Minimal Varieties, Proc. of Symp. in Pure Math. 27 (1975), 143-175. | MR 52 #1496 | Zbl 0328.49020
,[L2] The unknottedness of minimal embeddings, Inv. Math. 11 (1970), 183-187. | MR 44 #4651 | Zbl 0205.52002
,[LM] Spin Geometry (to appear).
and ,[LY] Scalar curvature, non-abelian group actions and the degree of symmetry of exotic spheres, Comm. Math. Helv. 49 (1974), 232-244. | MR 50 #11300 | Zbl 0297.57016
and ,[Li] Spineurs harmoniques, C.r. Acad. Sci. Paris, Sér. A-B, 257 (1963), 7-9. | MR 27 #6218 | Zbl 0136.18401
,[Lu] Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 229-256. | MR 48 #1250 | Zbl 0265.57009
,[MSY] Embedded minimal surfaces, exotic spheres and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982), 621-659. | Zbl 0521.53007
, and ,[M1] On manifolds homemorphic to the 7-sphere, Ann. of Math. (2) 64 (1956), 399-405. | MR 18,498d | Zbl 0072.18402
,[M2] Remarks concerning spin manifolds, "Differential Geometry and Combinatorial Topology", Princeton University Press, 1965, 55-62. | MR 31 #5208 | Zbl 0132.19602
,[M3] Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, 1965. | MR 37 #2239 | Zbl 0136.20402
,[M4] A Unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7. | MR 25 #5518 | Zbl 0108.36501
,[Mi] On the existence of positive scalar curvature metrics on non-simply-connected manifolds (to appear). | Zbl 0541.53034
,[Mor] Multiple Integrals and the Calculus of Variations, New York, Springer-Verlag, 1966. | MR 34 #2380 | Zbl 0142.38701
,[O] Bonneson-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979), 1-29. | MR 80h:52013 | Zbl 0404.52012
,[Sa] On a theorem of Burago-Toponogov (to appear). | Zbl 0512.53042
,[Sc] Topological Vector Spaces, N.Y., Springer-Verlag, 1971. | MR 49 #7722 | Zbl 0212.14001
,[S] A remark on minimal hypercones (to appear).
,[SY1] Existence of incompressible minimal surfaces and the topology of three dimensional manifolds of non-negative scalar curvature, Ann. of Math. 110 (1979), 127-142. | MR 81k:58029 | Zbl 0431.53051
and ,[SY2] On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. | MR 80k:53064 | Zbl 0423.53032
and ,[SY3] 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. | MR 83k:53060 | Zbl 0481.53036
and ,[SY4] Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature, Comm. Math. Helv. 39 (1976), 333-341. | MR 55 #11302 | Zbl 0361.53040
and ,[SY5]
and (to appear).[Si] Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105. | MR 38 #1617 | Zbl 0181.49702
,[T] Quelques propriétés globales des variétés différentiables, Comm. Math. Helv. 28 (1954), 17-86. | MR 15,890a | Zbl 0057.15502
,