Optimal $L^2$ Extensions of Openness Type and Related Topics
We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels. We describe a different approach to the Suita conjecture and it...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.437/ |
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| _version_ | 1825206276701814784 |
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| author | Xu, Wang Zhou, Xiangyu |
| author_facet | Xu, Wang Zhou, Xiangyu |
| author_sort | Xu, Wang |
| collection | DOAJ |
| description | We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels. We describe a different approach to the Suita conjecture and its generalizations, which is based on a log-concavity for certain minimal $L^2$ integrals. |
| format | Article |
| id | doaj-art-f3bedf292d054d328b65e369e838accb |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f3bedf292d054d328b65e369e838accb2025-02-07T11:07:00ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-03-01361G367968310.5802/crmath.43710.5802/crmath.437Optimal $L^2$ Extensions of Openness Type and Related TopicsXu, Wang0Zhou, Xiangyu1School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. ChinaInstitute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. ChinaWe establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels. We describe a different approach to the Suita conjecture and its generalizations, which is based on a log-concavity for certain minimal $L^2$ integrals.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.437/ |
| spellingShingle | Xu, Wang Zhou, Xiangyu Optimal $L^2$ Extensions of Openness Type and Related Topics Comptes Rendus. Mathématique |
| title | Optimal $L^2$ Extensions of Openness Type and Related Topics |
| title_full | Optimal $L^2$ Extensions of Openness Type and Related Topics |
| title_fullStr | Optimal $L^2$ Extensions of Openness Type and Related Topics |
| title_full_unstemmed | Optimal $L^2$ Extensions of Openness Type and Related Topics |
| title_short | Optimal $L^2$ Extensions of Openness Type and Related Topics |
| title_sort | optimal l 2 extensions of openness type and related topics |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.437/ |
| work_keys_str_mv | AT xuwang optimall2extensionsofopennesstypeandrelatedtopics AT zhouxiangyu optimall2extensionsofopennesstypeandrelatedtopics |