Generalized Suita conjectures with jets and weights
Xu, Wang1, 2; Zhou, Xiangyu3
1School of Mathematics, Sun Yat-sen University, Guangzhou 510275 (China)
2School of Mathematical Sciences, Peking University, Beijing 100871 (China)
3Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190 (China)
Annales de l'Institut Fourier, Online first, 27 p.

We survey different approaches to Suita’s conjecture and its various generalizations. We present a new and unified proof for generalized Suita conjectures with jets and weights, which is based on the concavity of certain minimal $L^2$ integrals and the necessary condition for linearity. Additionally, we provide some examples and counterexamples for the equalities in generalized Suita conjectures.

Nous passons en revue différentes approches de la conjecture de Suita et de ses diverses généralisations. Nous présentons une nouvelle preuve unifiée des conjectures généralisées de Suita avec jets et poids, basée sur la concavité de certaines $L^2$-intégrales minimales et la condition nécessaire de linéarité. De plus, nous donnons quelques exemples et contre-exemples pour les égalités dans les conjectures généralisées de Suita.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3756
Classification: 32A36, 30C40, 30C85
Keywords: Suita conjecture, Bergman kernel, logarithmic capacity, Azukawa indicatrix, Hartogs domain
Mots-clés : conjecture de Suita, noyau de Bergman, capacité logarithmique, indicatrice d’Azukawa, domaine de Hartogs

Xu, Wang  1 , 2 ; Zhou, Xiangyu  3

1 School of Mathematics, Sun Yat-sen University, Guangzhou 510275 (China)
2 School of Mathematical Sciences, Peking University, Beijing 100871 (China)
3 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190 (China) 
Xu, Wang; Zhou, Xiangyu. Generalized Suita conjectures with jets and weights. Annales de l'Institut Fourier, Online first, 27 p.
@unpublished{AIF_0__0_0_A44_0,
     author = {Xu, Wang and Zhou, Xiangyu},
     title = {Generalized {Suita} conjectures with jets and weights},
     journal = {Annales de l'Institut Fourier},
     year = {2026},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     doi = {10.5802/aif.3756},
     language = {en},
     note = {Online first},
}
TY  - UNPB
AU  - Xu, Wang
AU  - Zhou, Xiangyu
TI  - Generalized Suita conjectures with jets and weights
JO  - Annales de l'Institut Fourier
PY  - 2026
PB  - Association des Annales de l’institut Fourier
N1  - Online first
DO  - 10.5802/aif.3756
LA  - en
ID  - AIF_0__0_0_A44_0
ER  - 
%0 Unpublished Work
%A Xu, Wang
%A Zhou, Xiangyu
%T Generalized Suita conjectures with jets and weights
%J Annales de l'Institut Fourier
%D 2026
%V 0
%N 0
%I Association des Annales de l’institut Fourier
%Z Online first
%R 10.5802/aif.3756
%G en
%F AIF_0__0_0_A44_0

Cited by Sources: