Calabi-Yau metrics on C^n with tangent cone C × A1 are unique up to scaling and isometry.
Mazet, Minimal hypersurfaces asymptotic to Simons cones , J
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Uniqueness of some Calabi-Yau metrics on $\mathbf{C}^n$
Calabi-Yau metrics on C^n with tangent cone C × A1 are unique up to scaling and isometry.