Generalized $L^2$ extension theorem and a conjecture of Ohsawa

Guan, Qiʼan; Zhou, Xiangyu

Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 111-114.

Dans cet article, nous déterminons la constante optimale intervenant dans lʼestimée du théorème dʼextension $L^2$ généralisé de Ohsawa. Le résultat vaut pour les fibrés vectoriels holomorphes sur une classe de variétés complexes incluant à la fois les variétés de Stein et les variétés algébriques projectives complexes. Comme application, nous obtenons la solution dʼune conjecture correspondante dʼOhsawa.

In this paper, we determine the optimal constant in the estimate of Ohsawaʼs generalized $L^2$ extension theorem. The result holds for holomorphic vector bundles on a class of complex manifolds including both Stein manifolds and complex projective algebraic manifolds. As an application, we obtain a solution to a related conjecture of Ohsawa.

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