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Uniform lower bounds for the quotient invariant on the class of convex and C-convex domains. (arXiv:2401.05096v1 [math.CV])

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We establish explicit universal lower bounds for the quotient invariant on
the class of non-degenerate convex domains, as well as on the more general
class of non-degenerate $\mathbb{C}$-convex domains. The bounds we derive, for
the above mentioned classes in $\mathbb{C}^{n}$, only depend on the dimension
$n$ for a fixed $n\geq 2$. We then provide domain-dependent lower bounds for
the Carath\'eodory and Kobayashi-Eisenman volume elements on a bounded domain
$D \subset \mathbb{C}^{n}$, when $D$ belongs to either of those two
aforementioned categories.

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