论文标题
残留功能和扩展问题
Residue functions and Extension problems
论文作者
论文摘要
Demailly的“定性”扩展定理保证了在某些积极阳性假设下的某些子各种群体上的全体形态延伸的存在，但这是没有任何扩展的估计，尤其是当子方面的奇异基因座不空的地方是无空的，并且在那里均不扩展。残留功能是分析功能，可将$ l^2 $规范（或其单一基因座）上的$ l^2 $规范连接到$ l^2 $规范，并在环境空间上具有特定的权重。由猜想的“ DLT扩展”激励，本说明讨论了通过使用残留功能在一般情况下取回$ l^2 $估计的可能性。本说明还显示，通过索引$ 1 $定义的$ 1 $ -LC量化确实等于Ohsawa-takegoshi $ l^2 $扩展定理中的Ohsawa度量。
The "qualitative" extension theorem of Demailly guarantees existence of holomorphic extensions of holomorphic sections on some subvariety under certain positive-curvature assumption, but that comes without any estimate of the extensions, especially when the singular locus of the subvariety is non-empty and the holomorphic section to be extended does not vanish identically there. Residue functions are analytic functions which connect the $L^2$ norms on the subvarieties (or their singular loci) to $L^2$ norms with specific weights on the ambient space. Motivated by the conjectural "dlt extension", this note discusses the possibility of retrieving the $L^2$ estimates for the extensions in the general situation via the use of the residue functions. It is also shown in this note that the $1$-lc-measure defined via the residue function of index $1$ is indeed equal to the Ohsawa measure in the Ohsawa--Takegoshi $L^2$ extension theorem.
