Value-sharing of meromorphic functions on a Riemann surface

We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus, the complex plane.Comment: 15 page

Some uniqueness results related to the Br\"{u}ck Conjecture

Let f be a non-constant meromorphic function and a = a(z) be a small function of f. Under certain essential conditions, we obtained similar type conclusion of Bruck Conjecture, when f and its differential polynomial P[f] shares a with weight l. Our result improves and generalizes a recent result of Li, Yang, and Liu.Comment: 11 page