On the structure of manifolds with positive scalar curvature

@article{Schoen1979OnTS,
  title={On the structure of manifolds with positive scalar curvature},
  author={Richard M. Schoen and Shing-Tung Yau},
  journal={manuscripta mathematica},
  year={1979},
  volume={28},
  pages={159-183}
}
Publisher Summary This chapter discusses some recent results by Richard Schoen and Shing-Tung Yau on the structure of manifolds with positive scalar curvature. The chapter presents theorems which are felt to provide a more complete picture of manifolds with positive scalar curvature: (1) let M be a compact four-dimensional manifold with positive scalar curvature. Then there exists no continuous map with non-zero degree onto a compact K(π,1). (2) Let M be n-dimensional complete manifold with non… 
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References

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LetM be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass ofM as viewed from spatial infinity (the ADM mass) must be positive unlessM is the flat…
Existence of incompressible minimal surfaces and the topology of three - dimensional manifolds with
A multi-purpose handle-directed, manually propelled wheeled vehicle particularly well adapted for safe snow removal, load carrying, and similar labor saving tasks in rough and uncertain terrain; in…
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We extend our previous method of proving the positive-mass conjecture to prove the positive-action conjecture of Hawking for asymptotically Euclidean metric. This result is crucial in proving the…
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Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity.
  • R. Schoen, S. Yau
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1978
TLDR
This work finds new topological obstruction for three-dimensional Riemannian manifolds with nonnegative scalar curvature and turns out to be useful in studying the positive mass conjecture in general relativity.
Spin and Scalar Curvature in the Presence of a Fundamental Group. I
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