Automorphisms of braid groups on orientable surfaces

In this paper, we compute the automorphism groups Aut(Pn(∑)) and Aut(Bn(∑)) of braid groups Pn(∑) and Bn(∑) on every orientable surface ∑, which are isomorphic to group extensions of the extended mapping class group M n (∑) by the transvection subgroup except for a few cases. We also prove that Pn(∑) is always a characteristic subgroup of Bn(∑), unless ∑ is a twice-punctured sphere and n = 2.