An $L^2$ extension theorem with optimal estimate

Guan, Qiʼan; Zhou, Xiangyu

Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 137-141.

Dans cette note, nous présentons un théorème dʼextension $L^2$ avec estimation optimale, pour des fibrés vectoriels holomorphes semi-positifs dans le sens de Nakano. Ce résultat implique aussi des versions optimales pour lʼestimation de divers autres théorèmes dʼextension $L^2$. En application, nous obtenons la solution du cas dʼégalité dans une conjecture de Suita relative aux capacité logarithmiques de surfaces de Riemann ouvertes, ainsi que la solution de la conjecture de Suita généralisée, et la confirmation dʼun énoncé connu sous le nom de L-conjecture.

In this note, we establish an $L^2$ extension theorem with an optimal estimate for semi-positive vector bundles in the sense of Nakano. This result also implies optimal estimate versions of various $L^2$ extension theorems. Applications include a solution of the equality case in a conjecture of Suita on logarithmic capacities of open Riemann surface, as well as a solution of the extended Suita conjecture and a confirmation of the so-called L-conjecture.

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