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Title: Gaussian Cooling and $O^*(n^3)$ Algorithms for Volume and Gaussian Volume
Award ID(s):
1717349
PAR ID:
10113902
Author(s) / Creator(s):
;
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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  1. 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. 
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