[Conjectures généralisées de Suita avec jets et poids]
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.
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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
@unpublished{AIF_0__0_0_A44_0,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},
}
Xu, Wang; Zhou, Xiangyu. Generalized Suita conjectures with jets and weights. Annales de l'Institut Fourier, Online first, 28 p.
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