Gaussian Cooling and $O^*(n^3)$ Algorithms for Volume and Gaussian Volume
- Award ID(s):
- 1717349
- PAR ID:
- 10113902
- Date Published:
- Journal Name:
- SIAM Journal on Computing
- Volume:
- 47
- Issue:
- 3
- ISSN:
- 0097-5397
- Page Range / eLocation ID:
- 1237 to 1273
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, (2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, (3) a conjectural bound of $$\ell ^2$$ ℓ 2 -Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of 1-balls in the universal cover.more » « less
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