Pith. sign in

REVIEW

Geometric convergence of the K\"ahler-Ricci flow on complex surfaces of general type

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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

arxiv 1505.00705 v3 pith:FE6VBLHI submitted 2015-05-04 math.DG math.CV

Bin Guo , Jian Song , Ben Weinkove This is my paper · ORCID
classification math.DGmath.CV
keywords ahler-riccifloworbifoldahler-einsteingeneralmetricsurfacestype
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We show that on smooth minimal surfaces of general type, the K\"ahler-Ricci flow starting at any initial K\"ahler metric converges in the Gromov-Hausdorff sense to a K\"ahler-Einstein orbifold surface. In particular, the diameter of the evolving metrics is uniformly bounded for all time and the K\"ahler-Ricci flow contracts all the holomorphic spheres with $(-2)$ self-intersection number to isolated orbifold points. Our estimates do not require a priori the existence of an orbifold K\"ahler-Einstein metric on the canonical model.

Discussion (0). Continue with ORCID to comment.

Pith tools