Calabi Symmetry and the Continuity Method
Differential Geometry
2022-10-11 v1 Complex Variables
Abstract
We study the convergence and curvature blow up of La Nave and Tian's continuity method on a generalised Hirzebruch surface. We show that the Gromov-Hausdorff convergence is similar to that of the Kahler-Ricci flow and obtain curvature estimates. We also show that a general solution to the continuity method either exist or all times, or the scalar curvature blows up. This behavior is known to be exhibited by the Kahler-Ricci flow.
Keywords
Cite
@article{arxiv.2210.04546,
title = {Calabi Symmetry and the Continuity Method},
author = {Hosea Wondo},
journal= {arXiv preprint arXiv:2210.04546},
year = {2022}
}
Comments
18 pages, 1 figures. Any comments are welcomed