Marcelo Viana has conjectured that a smooth diffeomorphism admits a
physical measure if the Lyapunov exponents of its orbits in a full
volume set do not vanish. I will explain how a technique controlling
the continuity of Lyapunov exponents allows to prove this conjecture
in the case of smooth surface diffeomorphisms. This is a joint work
with Jérôme Buzzi and Omri Sarig.