Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 2nd Issue

Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics and has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in.

For each orientation-preserving nite group action on the closed orientable surface of genus 2, we determine its extendability over the handlebody of geuns 2 and over the 3-sphere; to do this we rst nd geometric generators.

By Andreev theorem acute-angled polyhedra of finite volume in a hyperbolic space H³ are uniquely determined by combinatorics of their 1-skeletons and dihedral angles. For a class of compact right- angled polyhedra and a class of ideal right-angled polyhedra estimates of volumes in terms of the number of vertices were obtained by Atkinson in 2009. In the present paper upper estimates for both classes are improved.