Some Properties and Applications of Bers Quasiforms on Riemann Surfaces
Abstract
Abstract 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.
Fields of Study & Subjects
Mathematics and Applications
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Journal of Geometric Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 5
- Publication date
- 15 April 2026
- Language
- EN