REVIEW 2 cited by
Collapsing geometry of hyperk\"ahler 4-manifolds and applications
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
Collapsing geometry of hyperk\"ahler 4-manifolds and applications
read the original abstract
We investigate the collapsing geometry of hyperk\"ahler 4-manifolds. As applications we prove two well-known conjectures in the field. (1) Any collapsed limit of unit-diameter hyperk\"ahler metrics on the K3 manifold is isometric to one of the following: the quotient of a flat 3-torus by an involution, a singular special K\"ahler metric on the 2-sphere, or the unit interval. (2) Any complete hyperk\"ahler 4-manifold with finite energy (i.e., gravitational instanton) is asymptotic to a model end at infinity.
Forward citations
Cited by 2 Pith papers
-
On toric self-dual Einstein gravitational instantons
Toric self-dual Einstein instantons with negative cosmological constant satisfying a global conformal Kähler extension condition are precisely the Calderbank-Pedersen-Singer multipole solutions.
-
Special Lagrangian submanifolds and circle collapse on K3
Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.