Abstract
Motivated by Witten’s spinor proof of the positive mass theorem, we analyze asymptotically constant harmonic spinors on complete asymptotically flat nonspin manifolds with nonnegative scalar curvature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnowitt R., Deser S., Misner C.: Coordinate invariance and energy expressions in General Relativity. Phys. Rev. 122, 997–1006 (1961)
Agmon, S.: Lectures on exponential decay of solutions of second order elliptic equations. Princeton, NJ: Princeton University Press, 1982
Baldwin, P.: L 2 solutions of Dirac equations. PhD Thesis, University of Cambridge, 1999
Bartnik R.: The mass of an asymptotically flat manifold. Comm. Pure Appl. Math. 39(5), 661–693 (1986)
Bray H.: Proof of the Riemannian Penrose inequality using the positive mass theorem. J. Diff. Geom. 59(2), 177–267 (2001)
Feldman E.: The geometry of immersions. I. Trans. Amer. Math. Soc. 120, 185–224 (1965)
Gray, A.: Tubes. Second edition, Progress in Mathematics 221, Basel: Birkhäuser Verlag, 2004
Gromov M., Lawson B.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Inst. Hautes Études Sci. Publ. Math. 58, 83–196 (1983)
Hirsch, M.: Differential topology. Graduate Texts in Mathematics, No. 33, New York-Heidelberg: Springer-Verlag, 1976
Lawson, B., Michelsohn, M.-L.: Spin geometry. Princeton, NJ: Princeton University Press, 1989
Lee J., Parker T.: The Yamabe problem. Bull. Amer. Math. Soc. (N.S.) 17(1), 37–91 (1987)
Lohkamp, J.: The higher dimensional positive mass theorem I. http://arxiv.org/abs/math/0608795v1 [math.DG], 2006
Milnor, J., Stasheff, J.: Characteristic Classes. Princeton, NJ: Princeton University Press, 1974
Mrowka, T.: Lecture notes for Geometry of Manifolds. MIT OpenCourseWare, http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/index.htm
Pardon W., Stern M.: \({L^2-\bar{\partial}}\) -cohomology of complex projective varieties. JAMS 4, 603–621 (1991)
Pardon W., Stern M.: Pure Hodge Structure on the L 2-cohomology of varieties with isolated singularities. J. Reine Angew. Math. 533, 55–80 (2001)
Parker T., Taubes C.: On Witten’s proof of the positive energy theorem. Commun. Math. Phys. 84(2), 223–238 (1982)
Schoen, R.: Personal communication
Schoen R.: On the proof of the positive mass conjecture in general relativity. J. Diff. Geom. 20(2), 479–495 (1984)
Schoen R., Yau S.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65(1), 45–76 (1979)
Steenrod, N.: The Topology of Fibre Bundles. Princeton Mathematical Series, Vol. 14, Princeton, NJ.: Princeton University Press, 1951
Trotman, D.: Stability of transversality to a stratification implies Whitney (a)-regularity. Invent. Math. 50, no. 3, 273–277 (1978/79)
Whitney H.: Tangents to an analytic variety. Ann. of Math. 81(3), 496–549 (1965)
Witten E.: A new proof of the positive energy theorem. Commun. Math. Phys. 80(3), 381–402 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by P. T. Chruściel
Rights and permissions
About this article
Cite this article
Degeratu, A., Stern, M. Witten Spinors on Nonspin Manifolds. Commun. Math. Phys. 324, 301–350 (2013). https://doi.org/10.1007/s00220-013-1804-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-013-1804-0