Existence of coupled K\"ahler-Einstein metrics using the continuity method
Differential Geometry
2017-05-04 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this paper we prove the existence of coupled K\"ahler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in the said case was proven by Hultgren and Nystr\"om using calculus of variations. We prove the result using the method of continuity. In the process of proving estimates, akin to the usual K\"ahler-Einstein metrics, we reduce existence in the Fano case to a C^0 estimate.
Cite
@article{arxiv.1609.02047,
title = {Existence of coupled K\"ahler-Einstein metrics using the continuity method},
author = {Vamsi Pritham Pingali},
journal= {arXiv preprint arXiv:1609.02047},
year = {2017}
}
Comments
Slightly modified the statement of theorem 1.3 (openness) and substantially corrected the proof