It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-1-3, author = {Nikolai Nikolov}, title = {Two remarks on the Suita conjecture}, journal = {Annales Polonici Mathematici}, volume = {113}, year = {2015}, pages = {61-63}, zbl = {1314.32004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-1-3} }
Nikolai Nikolov. Two remarks on the Suita conjecture. Annales Polonici Mathematici, Tome 113 (2015) pp. 61-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-1-3/