On the Ohsawa–Takegoshi L2 extension theorem and the twisted Bochner–Kodaira identity

Cauchy–Riemann meet Monge–Ampère

“…and the best constant one can get this way is 1.95388..., the same as the one obtained earlier in [59]. After [27], Guan and Zhou [57] proved various generalizations of Theorem 7.1 but used essentially the same ODE with two unknowns as (7.3) and got essentially the same solutions.…”

“…for some large absolute constant C. It was later improved in [25] and [59]. The optimal constant was eventually obtained in [27] where the following version of the Ohsawa-Takegoshi theorem also with optimal constant was proved: …”

Suita conjecture and the Ohsawa-Takegoshi extension theorem

“…We use Chen's idea in the proof of Theorem 2 below. It improves a related∂-estimate from [6] which gave Theorem 1 but only with the same constant as in [10]. This∂-estimate was one of the crucial improvements compared to [6].…”

“…This was later improved to C = 2 in [5], where the main tool was an estimate from [1]. A slightly better constant C = 1.954 was recently obtained in [10], see also [6] for a much simpler proof.…”

Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa

“…Our proof in [18] was based on the methods of [20] and [47]. In the present paper, we will consider some generalization of the above theorem.…”