# Degenerations of $\mathbf{C}^n$ and Calabi-Yau metrics

## TL;DR

This paper constructs numerous complete Calabi-Yau metrics on complex Euclidean spaces and near singularities, revealing new geometric structures with maximal volume growth and singular tangent cones at infinity.

## Contribution

It introduces new methods to construct Calabi-Yau metrics on f^n and near singularities, expanding the understanding of their geometric and asymptotic properties.

## Key findings

- Constructed infinitely many complete Calabi-Yau metrics on f^n for n b3 3.
- Established existence of metrics with maximal volume growth and singular tangent cones.
- Extended constructions to neighborhoods of singularities with singular cross sections.

## Abstract

We construct infinitely many complete Calabi-Yau metrics on $\mathbf{C}^n$ for $n \geq 3$, with maximal volume growth, and singular tangent cones at infinity. In addition we construct Calabi-Yau metrics in neighborhoods of certain isolated singularities whose tangent cones have singular cross section, generalizing work of Hein-Naber.