A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials (Q707567)

The paper gives the construction and discussion of a new conformally invariant pseudo-metric \(q_R\) on an arbitrary Riemann surface \(R\). The construction is done via integrable holomorphic quadratic differentials and it is closely related to an extremal problem on \(R\). Additionally, the author establishes a new characterization of uniform thickness of Riemann surfaces in terms of invariant metrics, and he eventually gives lower estimates of \(q_R\) in terms of the logarithmic capacity.