A solution of an $L^{2}$ extension problem with optimal estimate and applications

@article{Guan2013ASO,
  title={A solution of an \$L^\{2\}\$ extension problem with optimal estimate and applications},
  author={Qi’an Guan and Xiangyu Zhou},
  journal={arXiv: Complex Variables},
  year={2013}
}
In this paper, we prove an $L^2$ extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known $L^2$ extension theorems. As applications, we give proofs of a conjecture of Suita on the equality condition in Suita's conjecture, the so-called $L-$conjecture, and the extended Suita conjecture. As other applications, we give affirmative answer to a question by Ohsawa about limiting case for the extension operators between the weighted… 
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