Poincaré–Lelong equation

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In mathematics, the Poincaré–Lelong equation, studied by Lelong (1964), is the partial differential equation

$i\partial \overline \partial u=\rho$

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 662462
Lelong, Pierre (1964), "Fonctions entières (n variables) et fonctions plurisousharmoniques d'ordre fini dans Cⁿ", Journal d'Analyse Mathématique 12: 365–407, ISSN 0021-7670, MR 0166391

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