Open AccessComplete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity
Author(s) -
Richard Schoen,
Shing–Tung Yau
Publication year - 1979
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.76.3.1024
Subject(s) - scalar curvature , conjecture , curvature , action (physics) , general relativity , mathematics , mathematical physics , theory of relativity , prescribed scalar curvature problem , scalar (mathematics) , physics , sectional curvature , pure mathematics , theoretical physics , geometry , quantum mechanics
We find some integrability conditions for low-dimensional manifolds to admit metrics with nonnegative scalar curvature. In particular, we solve the positive action conjecture in general relativity in the affirmative.