  The classification of finite group-actions on closed surfaces of small genus
is well-known. In the present paper we are interested in the question of which
of these group-actions are bounding (extend to a compact 3-manifold with the
surface as its unique boundary component, e.g. to a handlebody) or
geometrically bounding (extend to a hyperbolic 3-manifold with totally geodesic
boundary), concentrating, as a typical case, on large group-actions on surfaces
of genus 3.
