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… 
ON THE STRUCTURE OF THE FUNDAMENTAL GROUP OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE
The aim of this paper is to study the structure of the fun- damental group of a closed oriented Riemannian manifold with positive scalar curvature. To be more precise, let M be a closed oriented
Simply connected manifolds of positive scalar curvature
Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M
Construction of manifolds of positive scalar curvature
We prove that a regular neighborhood of a codimension > 3 subcomplex of a manifold can be chosen so that the induced metric on its boundary has positive scalar curvature. A number of useful facts
Scalar curvature, covering spaces, and Seiberg-Witten theory.
The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalarcurvature Riemannian metrics g on M . (To be precise, one only
On the Structure of Complete Manifolds with Positive Scalar Curvature
One of the greatest contributions of Rauch in differential geometry is his famous work on manifolds with positive curvature. His comparison theorems, which are needed for his proof of the pinching
Metrics of positive scalar curvature on spheres and the Gromov-Lawson conjecture
Boguslaw Hajduk Institute of Mathematics, Wrociaw University, pl. Grunwaldzki 2/4, PL-50-384 Wrodaw, Poland 1. Introduction In [2] and [9] an ingenious procedure is given to construct a Riemannian
Geometry of three-dimensional manifolds with scalar curvature lower bound
. The paper concerns three-dimensional complete manifolds with scalar curvature bounded from below. One of the purposes is to establish a sharp comparison theorem for the bottom spectrum in the
The topology of scalar curvature
Given a smooth closed manifold M we study the space of Riemannian metrics of positive scalar curvature on M. A long-standing question is: when is this space non- empty (i.e. when does M admit a
The topology of positive scalar curvature
In this survey article, given a smooth closed manifold M we study the space of Riemannian metrics of positive scalar curvature on M. A long-standing question is: when is this space non-empty (i.e.
...
...

References

SHOWING 1-10 OF 15 REFERENCES
On the proof of the positive mass conjecture in general relativity
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
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.
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
Proof of the Positive-Action Conjecture in Quantum Relativity
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
...
...