Uniqueness of smooth radial balanced metrics on the disc

@article{30280,
   author = {Engliš, Miroslav},
   article_location = {Abingdon},
   article_number = {3},
   doi = {http://dx.doi.org/10.1080/17476933.2018.1454915},
   keywords = {Balanced metric; Bergman kernel; strictly pseudoconvex domain},
   language = {eng},
   issn = {1747-6933},
   journal = {Complex Variables and Elliptic Equations. An International Journal},
   title = {Uniqueness of smooth radial balanced metrics on the disc},
   url = {https://www.tandfonline.com/doi/abs/10.1080/17476933.2018.1454915?journalCode=gcov20},
   volume = {64},
   year = {2019}
}

TY  - JOUR
ID  - 30280
AU  - Engliš, Miroslav
PY  - 2019
TI  - Uniqueness of smooth radial balanced metrics on the disc
JF  - Complex Variables and Elliptic Equations. An International Journal
VL  - 64
IS  - 3
SP  - 519-540
EP  - 519-540
PB  - Taylor and Francis Ltd.
SN  - 17476933
KW  - Balanced metric
KW  - Bergman kernel
KW  - strictly pseudoconvex domain
UR  - https://www.tandfonline.com/doi/abs/10.1080/17476933.2018.1454915?journalCode=gcov20
L2  - https://www.tandfonline.com/doi/abs/10.1080/17476933.2018.1454915?journalCode=gcov20
N2  - We show that the usual Poincaré metric is the only radial balanced metric on the disc with not too wild boundary behaviour. Additionally, we identify explicitly all radial metrics with such boundary behaviour which satisfy the balanced condition as far as germs at the boundary are concerned. Related results for the annulus and the punctured disc are also established.
ER  - 

ENGLIŠ, Miroslav. Uniqueness of smooth radial balanced metrics on the disc. \textit{Complex Variables and Elliptic Equations. An International Journal}. Abingdon: Taylor and Francis Ltd., roč.~64, č.~3, s.~519-540. ISSN~1747-6933. doi:10.1080/17476933.2018.1454915. 2019.