Balanced metrics and Berezin quantization on Hartogs triangles

2021
journal article
article
8
dc.abstract.enIn this paper, we study balanced metrics and Berezin quantization on a class of Hartogs domains defined by Ωn={(z1,…,zn)∈Cn:|z1|<|z2|<⋯<|zn|<1} which generalize the so-called classical Hartogs triangle. We introduce a Kähler metric g(ν) associated with the Kähler potential Φn(z):=−∑n−1k=1νkln(|zk+1|2−|zk|2)−νnln(1−|zn|2) on Ωn. As main contributions, on one hand we compute the explicit form for Bergman kernel of weighted Hilbert space, and then, we obtain the necessary and sufficient condition for the metric g(ν) on the domain Ωn to be a balanced metric. On the other hand, by using the Calabi’s diastasis function, we prove that the Hartogs triangles admit a Berezin quantization.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorBi, Enchaopl
dc.contributor.authorSu, Guicong - 415322 pl
dc.date.accessioned2021-04-26T08:40:25Z
dc.date.available2021-04-26T08:40:25Z
dc.date.issued2021pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical273-285pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume200pl
dc.identifier.doi10.1007/s10231-020-00995-2pl
dc.identifier.eissn1618-1891pl
dc.identifier.issn0373-3114pl
dc.identifier.project2017/26/E/ST1/00723.1pl
dc.identifier.projectROD UJ / OPpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/269770
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.enHartogs trianglespl
dc.subject.enbalanced metricspl
dc.subject.enBerezin quantizationpl
dc.subtypeArticlepl
dc.titleBalanced metrics and Berezin quantization on Hartogs trianglespl
dc.title.journalAnnali di Matematica Pura ed Applicatapl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
In this paper, we study balanced metrics and Berezin quantization on a class of Hartogs domains defined by Ωn={(z1,…,zn)∈Cn:|z1|<|z2|<⋯<|zn|<1} which generalize the so-called classical Hartogs triangle. We introduce a Kähler metric g(ν) associated with the Kähler potential Φn(z):=−∑n−1k=1νkln(|zk+1|2−|zk|2)−νnln(1−|zn|2) on Ωn. As main contributions, on one hand we compute the explicit form for Bergman kernel of weighted Hilbert space, and then, we obtain the necessary and sufficient condition for the metric g(ν) on the domain Ωn to be a balanced metric. On the other hand, by using the Calabi’s diastasis function, we prove that the Hartogs triangles admit a Berezin quantization.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Bi, Enchao
dc.contributor.authorpl
Su, Guicong - 415322
dc.date.accessioned
2021-04-26T08:40:25Z
dc.date.available
2021-04-26T08:40:25Z
dc.date.issuedpl
2021
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.physicalpl
273-285
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
200
dc.identifier.doipl
10.1007/s10231-020-00995-2
dc.identifier.eissnpl
1618-1891
dc.identifier.issnpl
0373-3114
dc.identifier.projectpl
2017/26/E/ST1/00723.1
dc.identifier.projectpl
ROD UJ / OP
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/269770
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri*
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subject.enpl
Hartogs triangles
dc.subject.enpl
balanced metrics
dc.subject.enpl
Berezin quantization
dc.subtypepl
Article
dc.titlepl
Balanced metrics and Berezin quantization on Hartogs triangles
dc.title.journalpl
Annali di Matematica Pura ed Applicata
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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