## 329 Citations

### On the Generalized Geroch Conjecture for Complete Spin Manifolds

- MathematicsChinese Annals of Mathematics, Series B
- 2022

Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold, the authors show that the connected sum M#W admits no complete metric of positive scalar…

### An Enlargeability Obstruction for Spacetimes with both Big Bang and Big Crunch

- Mathematics
- 2021

Given a spacelike hypersurface M of a time-oriented Lorentzian manifold (M,g), the pair (g, k) consisting of the induced Riemannian metric g and the second fundamental form k is known as initial data…

### Deformations of Q-curvature I

- MathematicsCalculus of Variations and Partial Differential Equations
- 2016

In this article, we investigate deformation problems of Q-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the Q-singular space, which was introduced by…

### Rigid comparison geometry for Riemannian bands and open incomplete manifolds

- Mathematics
- 2022

. Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either…

### RECENT RESULTS CONCERNING TOPOLOGICAL OBSTRUCTIONS TO POSITIVE SCALAR CURVATURE

- Mathematics
- 2022

. We survey recent work on topological obstructions to positive scalar curvature. In particular, we discuss the proofs by the authors and by Gromov that an a closed aspherical n -manifold does not…

### Conjectures on Convergence and Scalar Curvature

- Mathematics
- 2021

Here we survey the compactness and geometric stability conjectures formulated by the participants at the 2018 IAS Emerging Topics Workshop on Scalar Curvature and Convergence. We have tried to survey…

### Width, Largeness and Index Theory

- Mathematics
- 2020

In this note, we review some recent developments related to metric aspect of scalar curvature from the point of view of index theory for Dirac operators. In particular, we revisit index-theoretic…

### Positive Scalar Curvature on Foliations:The Enlargeability

- MathematicsGeometric Analysis
- 2020

We generalize the famous result of Gromov and Lawson on the nonexistence of metric of positive scalar curvature on enlargeable manifolds to the case of foliations, without using index theorems on…

### Deformations of positive scalar curvature metrics on 3-manifolds with mean-convex boundary

- Mathematics
- 2019

We give a complete topological characterization of those compact 3-manifolds that support Riemannian metrics of positive scalar curvature and mean-convex boundary. In any such case, we prove that the…

## References

SHOWING 1-10 OF 20 REFERENCES

### Acad. Sci. Paris Ser. A-B

- Acad. Sci. Paris Ser. A-B
- 1963

### Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series

- Mathematics
- 1956

In The following lectures we shall give a brief sketch of some representative parts of certain investigations that have been undertaken during the last five years. The center of these investigations…

### STABLE MAPPINGS OF FOLIATIONS INTO MANIFOLDS

- Mathematics
- 1969

In this article we shall study the topological properties of sheaves of germs of mappings, and for such sheaves construct an analog of obstruction theory. The method proposed makes it possible to…

### Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres

- Mathematics
- 1974

It is proved that if a compact manifold admits a smooth action by a compact, connected, non-abelian Lie group, then it admits a metric of positive scalar curvature. This result is used to prove that…

### On the structure of manifolds with positive scalar curvature

- Mathematics
- 1979

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…