Year: 2026
Type: preprint
Abstract: We study complete noncompact Ricci-flat Kähler manifolds. In the case of Euclidean volume growth, we prove that the underlying complex manifold is naturally quasi-projective and that the asymptotic cone is unique. Moreover, we establish no semistability at infinity and prove convergence to the asymptotic cone at a polynomial rate. In the case of sub-Euclidean volume growth, we construct complete Ricci-flat Kähler threefolds with bounded sectional curvature and finite topological type that admit no Kähler compactification.
Source: arXiv (Cornell University)
Authors: Sun, Song, Zhang, Junsheng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223213450