Some Properties and Applications of Bers Quasiforms on Riemann Surfaces

We describe some properties of the Bers quasiform on a compact Riemann surface in the Schottky sewing scheme. Our main results are: (i) the expansion of meromorphic differential forms in terms of holomorphic forms and derivatives of the Bers quasiform, (ii) power series expansions in the Schottky sewing parameters of the Bers quasiform and holomorphic forms, (iii) a novel differential operator which acts on meromorphic forms in several variables which we apply in deriving differential equations for classical objects such as the bidifferential of the second kind, the projective connection, holomorphic 1-forms and the prime form.