In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L<sup>2</sup> extension. The conjecture states the following:
It was first proved by for the bounded plane domain and then completely in a more generalized version by . Also, another proof of the Suita conjecture and some examples of its generalization to several complex variables (the multi (high) - dimensional Suita conjecture) were given in and . The multi (high) - dimensional Suita conjecture fails in non-pseudoconvex domains. This conjecture was proved through the optimal estimation of the OhsawaâÂÂTakegoshi L<sup>2</sup> extension theorem.