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Fully non-linear elliptic equations on noncompact complex manifolds
Published 17 Dec 2025 in math.DG and math.AP | (2512.15350v1)
Abstract: In this paper, we obtain the a priori estimates and the existence results for solutions of a general class of fully non-linear equations on noncompact Kähler and Hermitian manifolds. As geometric applications, we can construct Kähler metrics with some prescribed volume forms on strictly pseudoconvex domains; and we can construct complete Chern-Einstein metrics on Hermitian manifolds with bounded geometry.
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