Calabi-Yau metrics of Calabi type with polynomial rate of convergence

TL;DR

This paper constructs new complete Calabi-Yau metrics on certain complex manifolds, demonstrating their polynomial convergence to a model space and proving their uniqueness within a cohomology class.

Contribution

It introduces a class of Calabi-Yau metrics with polynomial convergence rates and establishes their uniqueness in a fixed cohomology class.

Findings

Constructed new complete Calabi-Yau metrics with polynomial decay.

Proved the uniqueness of these metrics within a fixed cohomology class.

Abstract

We present new complete Calabi-Yau metrics defined on the complement of a smooth anticanonical divisor with ample normal bundle, approaching the Calabi model space at a polynomial rate. Moreover, we establish the uniqueness of this type of Calabi-Yau metric within a fixed cohomology class.