Positive scalar curvature and the Dirac operator on complete riemannian manifolds
Publications Mathématiques de l'IHÉS, Tome 58 (1983), pp. 83-196. 
@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},
     pages = {83--196},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {58},
     year = {1983},
     mrnumber = {720933},
     zbl = {0538.53047},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1983__58__83_0/}
}
TY  - JOUR
AU  - Gromov, Mikhael
AU  - Lawson, H. Blaine
TI  - Positive scalar curvature and the Dirac operator on complete riemannian manifolds
JO  - Publications Mathématiques de l'IHÉS
PY  - 1983
SP  - 83
EP  - 196
VL  - 58
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1983__58__83_0/
LA  - en
ID  - PMIHES_1983__58__83_0
ER  - 
%0 Journal Article
%A Gromov, Mikhael
%A Lawson, H. Blaine
%T Positive scalar curvature and the Dirac operator on complete riemannian manifolds
%J Publications Mathématiques de l'IHÉS
%D 1983
%P 83-196
%V 58
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1983__58__83_0/
%G en
%F 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://www.numdam.org/item/PMIHES_1983__58__83_0/

[Ag] S. Agmon, Elliptic Boundary Value Problems, Van Nostrand, 1965. | MR | Zbl

[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. | MR | Zbl

[A] M. F. Atiyah, Elliptic operators, discrete groups and Von Neumann algebras, Astérisque, vol. 32-33, Société Math. de France, 1976, 43-72. | MR | Zbl

[ABS] M. F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (Suppl. 1) (1964), 3-38. | MR | Zbl

[AH] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Symp. Pure Math. A.M.S. III (1961), 7-38. | MR | Zbl

[ASI] M. F. Atiyah and I. Singer, The index of elliptic operators I, Ann. of Math. 87 (1968), 484-530. | MR | Zbl

[ASIII] M. F. Atiyah and I. Singer, The index of elliptic operators III, Ann. of Math. 87 (1968), 546-604. | MR | Zbl

[ASV] M. F. Atiyah and I. Singer, The index of elliptic operators V, Ann. of Math. 93 (1971), 139-149. | MR | Zbl

[AS] M. F. Atiyah and I. Singer, Index Theory for skew-adjoint Fredholm operators, Publ. Math. I.H.E.S. 37, (1969), 1-26. | Numdam | MR | Zbl

[B1] L. Bérard Bergery, La courbure scalaire des variétés riemanniennes, Sém. Bourbaki, exposé n° 556, juin 1980, Springer Lecture Notes 842 (1981), 225-245. | Numdam | MR | Zbl

[B2] L. Bérard Bergery, Scalar curvature and isometry group (to appear).

[BT] Yu. D. Burago and V. A. Toponagov, On 3-dimensional riemannian spaces with curvature bounded above, Math. Zametki 13 (1973), 881-887. | MR | Zbl

[BZ] Yu. D. Burago and V. A. Zagallar, Geometric Inequalities (in Russian), Leningrad, 1980. | Zbl

[CF] I. Chavel and E. Feldman, Isoperimetric inequalities on curved surfaces (to appear). | Zbl

[CG] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom. 6 (1917), 119-128. | MR | Zbl

[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. | MR | Zbl

[F1] H. Federer, Geometric Measure Theory, N.Y., Springer Verlag, 1969. | MR | Zbl

[F2] H. Federer, Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974), 351-407. | MR | Zbl

[FF] H. Federer and W. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458-520. | MR | Zbl

[Fia] F. Fiala, Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comm. Math. Helv. 13 (1941), 293-346. | JFM | MR | Zbl

[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. | MR | Zbl

[Fl] W. Fleming, On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962), 69-90. | MR | Zbl

[Gao] Z. Gao, Thesis, Stony Brook, 1982.

[G] M. Gromov, Filling riemannian manifolds, J. Diff. Geom. 18 (1983), 1-147. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[HS] R. Hardt and L. Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. 110 (1979), 439-486. | MR | Zbl

[Ha] P. Hartman, Geodesic parallel coordinates in the large, Amer. J. Math. 86 (1964), 705-727. | MR | Zbl

[H] N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | MR | Zbl

[I] V. K. Ionin, Isoperimetric and certain other inequalities for a manifold of bounded curvature, Sibirski Math. J. 10 (1969), 329-342. | MR | Zbl

[K] J. Kazdan, Deforming to positive scalar curvature on complete manifolds, Math. Ann. 261 (1982), 227-234. | MR | Zbl

[KW] J. Kazdan and F. Warner, Prescribing curvatures, Proc. of Symp. in Pure Math. 27 (1975), 309-319. | MR | Zbl

[KN] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, N.Y., Interscience, 1963. | MR | Zbl

[L1] H. B. Lawson Jr., Minimal Varieties, Proc. of Symp. in Pure Math. 27 (1975), 143-175. | MR | Zbl

[L2] H. B. Lawson Jr., The unknottedness of minimal embeddings, Inv. Math. 11 (1970), 183-187. | MR | Zbl

[LM] H. B. Lawson Jr. and M. L. Michelsohn, Spin Geometry (to appear).

[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. | MR | Zbl

[Li] A. Lichnerowicz, Spineurs harmoniques, C.r. Acad. Sci. Paris, Sér. A-B, 257 (1963), 7-9. | MR | Zbl

[Lu] G. Lusztig, Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 229-256. | MR | Zbl

[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. | Zbl

[M1] J. Milnor, On manifolds homemorphic to the 7-sphere, Ann. of Math. (2) 64 (1956), 399-405. | MR | Zbl

[M2] J. Milnor, Remarks concerning spin manifolds, "Differential Geometry and Combinatorial Topology", Princeton University Press, 1965, 55-62. | MR | Zbl

[M3] J. Milnor, Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, 1965. | MR | Zbl

[M4] J. Milnor, A Unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7. | MR | Zbl

[Mi] T. Miyazaki, On the existence of positive scalar curvature metrics on non-simply-connected manifolds (to appear). | Zbl

[Mor] C. B. Morrey, Multiple Integrals and the Calculus of Variations, New York, Springer-Verlag, 1966. | MR | Zbl

[O] R. Osserman, Bonneson-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979), 1-29. | MR | Zbl

[Sa] T. Sakai, On a theorem of Burago-Toponogov (to appear). | Zbl

[Sc] H. H. Schaefer, Topological Vector Spaces, N.Y., Springer-Verlag, 1971. | MR | Zbl

[S] R. Schoen, A remark on minimal hypercones (to appear).

[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. | MR | Zbl

[SY2] R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[SY5] R. Schoen and S. T. Yau (to appear).

[Si] J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105. | MR | Zbl

[T] R. Thom, Quelques propriétés globales des variétés différentiables, Comm. Math. Helv. 28 (1954), 17-86. | MR | Zbl