REVIEW 1 cited by
Minimal 2-Spheres and Optimal Foliations in 3-Spheres with Arbitrary Metric
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Minimal 2-Spheres and Optimal Foliations in 3-Spheres with Arbitrary Metric
read the original abstract
In this paper, we prove that the $3$-sphere endowed with an arbitrary Riemannian metric either contains at least two embedded minimal $2$-spheres or admits an optimal foliation by $2$-spheres. This generalizes recent results by Haslhofer-Ketover (Duke Math. J. 2019), where the existence of optimal foliations and minimal $2$-spheres has been established under the additional assumption that the metric is generic. In light of recent examples by Wang-Zhou, where min-max for some non-bumpy metrics on the 3-sphere produces higher multiplicities, our results are in a certain sense sharp.
Forward citations
Cited by 1 Pith paper
-
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric
Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.