Abstract

In this note, we establish an L2 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 L2 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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