@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},
year = {1983},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {58},
mrnumber = {720933},
zbl = {0538.53047},
language = {en},
url = {https://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 Etudes Scientifiques UR - https://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 Etudes Scientifiques %U https://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. https://www.numdam.org/item/PMIHES_1983__58__83_0/
[Ag] , Elliptic Boundary Value Problems, Van Nostrand, 1965. | Zbl | MR
[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. | Zbl | MR
[A] , Elliptic operators, discrete groups and Von Neumann algebras, Astérisque, vol. 32-33, Société Math. de France, 1976, 43-72. | Zbl | MR | Numdam
[ABS] , and , Clifford modules, Topology 3 (Suppl. 1) (1964), 3-38. | Zbl | MR
[AH] and , Vector bundles and homogeneous spaces, Proc. Symp. Pure Math. A.M.S. III (1961), 7-38. | Zbl | MR
[ASI] and , The index of elliptic operators I, Ann. of Math. 87 (1968), 484-530. | Zbl | MR
[ASIII] and , The index of elliptic operators III, Ann. of Math. 87 (1968), 546-604. | Zbl | MR
[ASV] and , The index of elliptic operators V, Ann. of Math. 93 (1971), 139-149. | Zbl | MR
[AS] and , Index Theory for skew-adjoint Fredholm operators, Publ. Math. I.H.E.S. 37, (1969), 1-26. | Zbl | MR | Numdam
[B1] , La courbure scalaire des variétés riemanniennes, Sém. Bourbaki, exposé n° 556, juin 1980, Springer Lecture Notes 842 (1981), 225-245. | Zbl | MR | Numdam
[B2] , Scalar curvature and isometry group (to appear).
[BT] and , On 3-dimensional riemannian spaces with curvature bounded above, Math. Zametki 13 (1973), 881-887. | Zbl | MR
[BZ] and , Geometric Inequalities (in Russian), Leningrad, 1980. | Zbl
[CF] and , Isoperimetric inequalities on curved surfaces (to appear). | Zbl
[CG] and , The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom. 6 (1917), 119-128. | Zbl | MR
[CY] and , Differential equations on riemannian manifolds and their geometric applications, Comm. Pure and Appl. Math. 28 (1975), 333-354. | Zbl | MR
[F1] , Geometric Measure Theory, N.Y., Springer Verlag, 1969. | Zbl | MR
[F2] , Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974), 351-407. | Zbl | MR
[FF] and , Normal and integral currents, Ann. of Math. 72 (1960), 458-520. | Zbl | MR
[Fia] , Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comm. Math. Helv. 13 (1941), 293-346. | Zbl | MR | JFM
[F-CS] and , The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature, Comm. Pure and Appl. Math. 33 (1980), 199-211. | Zbl | MR
[Fl] , On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962), 69-90. | Zbl | MR
[Gao] , Thesis, Stony Brook, 1982.
[G] , Filling riemannian manifolds, J. Diff. Geom. 18 (1983), 1-147. | Zbl | MR
[GL1] and , Spin and scalar curvature in the presence of a fundamental group, Ann. of Math. 111 (1980), 209-230. | Zbl | MR
[GL2] and , The classification of simply-connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434. | Zbl | MR
[HS] and , Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. 110 (1979), 439-486. | Zbl | MR
[Ha] , Geodesic parallel coordinates in the large, Amer. J. Math. 86 (1964), 705-727. | Zbl | MR
[H] , Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | Zbl | MR
[I] , Isoperimetric and certain other inequalities for a manifold of bounded curvature, Sibirski Math. J. 10 (1969), 329-342. | Zbl | MR
[K] , Deforming to positive scalar curvature on complete manifolds, Math. Ann. 261 (1982), 227-234. | Zbl | MR
[KW] and , Prescribing curvatures, Proc. of Symp. in Pure Math. 27 (1975), 309-319. | Zbl | MR
[KN] and , Foundations of Differential Geometry, N.Y., Interscience, 1963. | Zbl | MR
[L1] , Minimal Varieties, Proc. of Symp. in Pure Math. 27 (1975), 143-175. | Zbl | MR
[L2] , The unknottedness of minimal embeddings, Inv. Math. 11 (1970), 183-187. | Zbl | MR
[LM] and , Spin Geometry (to appear).
[LY] and , Scalar curvature, non-abelian group actions and the degree of symmetry of exotic spheres, Comm. Math. Helv. 49 (1974), 232-244. | Zbl | MR
[Li] , Spineurs harmoniques, C.r. Acad. Sci. Paris, Sér. A-B, 257 (1963), 7-9. | Zbl | MR
[Lu] , Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 229-256. | Zbl | MR
[MSY] , and , Embedded minimal surfaces, exotic spheres and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982), 621-659. | Zbl
[M1] , On manifolds homemorphic to the 7-sphere, Ann. of Math. (2) 64 (1956), 399-405. | Zbl | MR
[M2] , Remarks concerning spin manifolds, "Differential Geometry and Combinatorial Topology", Princeton University Press, 1965, 55-62. | Zbl | MR
[M3] , Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, 1965. | Zbl | MR
[M4] , A Unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7. | Zbl | MR
[Mi] , On the existence of positive scalar curvature metrics on non-simply-connected manifolds (to appear). | Zbl
[Mor] , Multiple Integrals and the Calculus of Variations, New York, Springer-Verlag, 1966. | Zbl | MR
[O] , Bonneson-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979), 1-29. | Zbl | MR
[Sa] , On a theorem of Burago-Toponogov (to appear). | Zbl
[Sc] , Topological Vector Spaces, N.Y., Springer-Verlag, 1971. | Zbl | MR
[S] , A remark on minimal hypercones (to appear).
[SY1] and , Existence of incompressible minimal surfaces and the topology of three dimensional manifolds of non-negative scalar curvature, Ann. of Math. 110 (1979), 127-142. | Zbl | MR
[SY2] and , On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. | Zbl | MR
[SY3] and , 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. | Zbl | MR
[SY4] and , Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature, Comm. Math. Helv. 39 (1976), 333-341. | Zbl | MR
[SY5] and (to appear).
[Si] , Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105. | Zbl | MR
[T] , Quelques propriétés globales des variétés différentiables, Comm. Math. Helv. 28 (1954), 17-86. | Zbl | MR
