On the ∂—-Equation with <i>L</i>2 Estimates on Singular Complex Spaces-Reference-Cited by-同舟云学术

On the ∂—-Equation with L2 Estimates on Singular Complex Spaces

Published:2024-04-22 Issue:12 Volume:2024 Page:9808-9826
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Li Zhenqian¹,Li Zhi²,Zhou Xiangyu³

Affiliation:

1. School of Mathematics and Computational Science , Xiangtan University, Xiangtan 411105, China

2. School of Science , Beijing University of Posts and Telecommunications, Beijing 100876, China

3. Institute of Mathematics , Academy of Mathematics and Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China

Abstract

Abstract In this paper, we present the unsolvability of $\overline \partial $-equation with weighted $L^{2}$ estimates involved curvature terms on any singular normal complex space in general. Moreover, in the non-normal case, we also give a complete description on $L^{2}$-solvability of the $\overline \partial $-equation with weighted $L^{2}$ estimates for plane curve singularities and their variants in the higher dimension.

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/article-pdf/2024/12/9808/58270733/rnae076.pdf

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