TL;DR
This paper investigates the set of volumes of constant scalar curvature one metrics on atoroidal three-manifolds, proving the supremum is infinite using minimal surfaces, Thurston norm, and new conformal invariants.
Contribution
It introduces new conformal invariants and proves the supremum of volumes is infinite for these manifolds, advancing understanding of scalar curvature metrics.
Findings
Supremum of volume set is infinite.
Introduces new conformal invariants.
Uses minimal surfaces and Thurston norm in proofs.
Abstract
We study the set of volumes of constant scalar curvature one metrics on an atoroidal three-manifold.The infinum of this set is believed to be attained at a hyperbolic metric. We prove that the supremum of this set is always infinity. The technique is: minimal surfaces, Thurston norm in homology and new conformal invariants.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsearthquake and tectonic studies · Geomagnetism and Paleomagnetism Studies · Geological and Geophysical Studies