REVIEW 3 cited by
Positive mass theorems of ALF and ALG manifolds
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
Positive mass theorems of ALF and ALG manifolds
abstract
In this paper, we want to prove positive mass theorems for ALF and ALG manifolds with model spaces $\mathbb R^{n-1}\times \mathbb S^1$ and $\mathbb R^{n-2}\times \mathbb T^2$ respectively in dimensions no greater than $7$ (Theorem \ref{ALFPMT0}). { Different from the compatibility condition for spin structure in \cite[Theorem 2]{minerbe2008a}, we show that some type of incompressible condition for $\mathbb S^1$ and $\mathbb T^2$ is enough to guarantee the nonnegativity of the mass.} As in the asymptotically flat case, we reduce the desired positive mass theorems to those ones concerning non-existence of positive scalar curvature metrics on closed manifolds coming from generalize surgery to $n$-torus. { Finally, we investigate certain fill-in problems and obtain an optimal bound for total mean curvature of admissible fill-ins for flat product $2$-torus $\mathbb S^1(l_1)\times \mathbb S^1(l_2)$.}
Forward citations
Cited by 3 Pith papers
-
A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of toric ALE or ALF 4-manifolds with nonnegative scalar curvature is at least the mass of the corresponding toric gravitational instanton plus a term from its conical defects, with equality only when the mani...
-
A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of any toric ALE/ALF 4-manifold with nonnegative scalar curvature is at least the mass of its corresponding toric gravitational instanton, corrected by conical angle defects, and equality holds only for the i...
-
Mass Lower Bounds for Asymptotically Locally Flat Manifolds
For ALF 4-manifolds with an almost free circle symmetry and nonnegative scalar curvature, mass is nonnegative and at least (ℓ/16) times the degree of the asymptotic circle bundle; in the AF case, homology-trivial coor...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.