What type of geological activity is common close to oceanic trenches where subduction is taking place.?

The answer is convergent plate boundaries. Convergent of two plates depends on the types of crust that are colliding. Convergence can take place between two slabs of continental lithosphere, two slabs of oceanic lithosphere or between one continental and one oceanic slab. Oftenly when two plates collide one or both are destroyed nd when oceanic crust converges with continental crust the denser oceanic plate plunges beneath the continental plate.