Isoperimetric inequality for nearly spherical domains in the Bergman ball double struck upper B 2$\mathbb{B}_2$ 𝔹 2

Source abstract

We prove a quantitative isoperimetric inequality for nearly spherical domains in the Bergman ball in double struck upper C 2 $\mathbb{C}^2$ ℂ 2 . We prove a Fuglede-type theorem for such sets. This result is a counterpart of a similar result obtained for the hyperbolic unit ball, and it provides the first result on the isoperimetric phenomenon in the Bergman ball.