Dans le présent article, nous montrons que étant donné une variété compacte de kählérienne avec une métrique de kählérienne (pas nécessairement une métrique de Hodge) , et une sous-variété complexe de dimension positif, si a une structure de rétraction holomorphe dans , alors toute fonction quasi-plurisousharmonique sur telle que avec peut être étendue é une fonction quasi-plurisousharmonique sur , telle que pour quelques . Ceci donne une réponse partielle à une question soulevée par Coman–Guedj–Zeriahi [4].
In the present paper, we show that given a compact Kähler manifold with a Kähler metric (not necessarily Hodge metric) , and a complex submanifold of positive dimension, if has a holomorphic retraction structure in , then any quasi-plurisubharmonic function on such that with can be extended to a quasi-plurisubharmonic function on , such that for some . This gives a partial answer to a question raised by Coman–Guedj–Zeriahi [4].
Accepté le :
Publié le :
Jiafu Ning 1 ; Zhiwei Wang 2 ; Xiangyu Zhou 3
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@article{AFST_2024_6_33_1_183_0, author = {Jiafu Ning and Zhiwei Wang and Xiangyu Zhou}, title = {On the extension of {K\"ahler} currents on compact {K\"ahler} manifolds: holomorphic retraction case}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {183--195}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 33}, number = {1}, year = {2024}, doi = {10.5802/afst.1767}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1767/} }
TY - JOUR AU - Jiafu Ning AU - Zhiwei Wang AU - Xiangyu Zhou TI - On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2024 SP - 183 EP - 195 VL - 33 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1767/ DO - 10.5802/afst.1767 LA - en ID - AFST_2024_6_33_1_183_0 ER -
%0 Journal Article %A Jiafu Ning %A Zhiwei Wang %A Xiangyu Zhou %T On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2024 %P 183-195 %V 33 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1767/ %R 10.5802/afst.1767 %G en %F AFST_2024_6_33_1_183_0
Jiafu Ning; Zhiwei Wang; Xiangyu Zhou. On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 1, pp. 183-195. doi : 10.5802/afst.1767. https://afst.centre-mersenne.org/articles/10.5802/afst.1767/
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