Meromorphic $$L^2$$ functions on flat surfaces

Meromorphic Functions on Certain Riemann Surfaces

1. Throughout the paper we shall denote by R a Riemann surface. For a domain Í2 in P, we represent by AB(Q) the class of all the singlevalued bounded analytic functions on the closure Ü. For a meromorphic function / on a domain ß, we use the notation viw\f, Q.) to express the number of times that/ attains w in ß. Definition 1. We say that REWIb if the maximum principle suplen \fip)\ =sup3,ean \...

Lectures on meromorphic flat connections

These notes form an extended version of a minicourse delivered in Université de Montréal (June 2002) within the framework of a NATO workshop “Normal Forms, Bifurcations and Finiteness Problems in Differential Equations”. The focus is on Poincaré–Dulac theory of “Fuchsian” (logarithmic) singularities of integrable systems, with applications to problems on zeros of Abelian integrals in view.

Good formal structures for flat meromorphic connections, I: Surfaces

We prove existence of good formal structures for flat meromorphic connections on surfaces after suitable blowing up; this verifies a conjecture of Sabbah, and extends a result of Mochizuki for algebraic connections. Our proof uses a numerical criterion, in terms of spectral behavior of differential operators, under which one can obtain a decomposition of a formal flat connection in arbitrary di...

On Analytic Surfaces with Two Independent Meromorphic Functions.

Good formal structure for meromorphic flat connections on smooth projective surfaces

We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.