Families of singular Chern-Ricci flat metrics
Chung-Ming Pan
TL;DR
This paper establishes uniform a priori estimates for degenerate complex Monge-Ampère equations on hermitian varieties, extending previous results and enabling analysis of Chern-Ricci flat potentials during conifold transitions.
Contribution
It generalizes a theorem to hermitian contexts and applies it to study the boundedness of Chern-Ricci flat potentials in conifold transitions.
Findings
Proved uniform a priori estimates for degenerate complex Monge-Ampère equations.
Extended Di Nezza-Guedj-Guenancia theorem to hermitian varieties.
Applied results to analyze Chern-Ricci flat potentials in conifold transitions.
Abstract
We prove uniform a priori estimates for degenerate complex Monge-Amp\`ere equations on a family of hermitian varieties. This generalizes a theorem of Di Nezza-Guedj-Guenancia to hermitian contexts. The main result can be applied to study the uniform boundedness of Chern-Ricci flat potentials in conifold transitions.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics