In mathematics, the Poincaré–Lelong equation, studied by Lelong (1964), is the partial differential equation
i ∂ ∂ ¯ u = ρ {\displaystyle i\partial {\overline {\partial }}u=\rho }
on a Kähler manifold, where ρ is a positive (1,1)-form.
References Mok, Ngaiming; Siu, Yum Tong; Yau, Shing Tung (1981), "The Poincaré–Lelong equation on complete Kähler manifolds", Compositio Mathematica, 44 (1): 183–218, ISSN 0010-437X, MR 0662462 Lelong, Pierre (1964), "Fonctions entières (n variables) et fonctions plurisousharmoniques d'ordre fini dans Cn", Journal d'Analyse Mathématique, 12: 365–407, doi:10.1007/bf02807441, ISSN 0021-7670, MR 0166391