Yau's compactification conjecture for complete Ricci-flat Kähler manifolds

Let MM be a complete Ricci-flat Kähler manifold. Yau's compactification conjecture. MM can be compactified into a compact complex manifold by adding a divisor at infinity. This conjecture concerns the relationship between the asymptotic geometry of complete Ricci-flat Kähler manifolds and compact complex geometry; the source gives no resolution status.

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Primary source

Mingyang Li and Song Sun, “Geometry of gravitational instantons”, arXiv:2606.10443 (2026).

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