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Quasi-isometry and deformations of Calabi-Yau manifolds (1207.1182v2)
Published 5 Jul 2012 in math.DG and math.AG
Abstract: We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of K\"ahler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of holomorphic $(n,0)$-forms on the deformation spaces of Calabi-Yau manifolds. Similar constructions are also applied to the deformation spaces of compact K\"ahler manifolds.