Uniformizable Singular Projective Structures on Riemann Surface Orbifolds

• Type: Article in International Scientific Journal
• Date: 2025

Authors

Ahmed Elshafei (Author) Other; Julio Rebelo (Author) Other; Helena Reis (Author) FEP

Journal

Title: Journal of Geometric Analysis

Vol. 35

ISSN: 1050-6926

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-018-FG4

DOI: 10.1007/s12220-025-01963-z

Abstract (EN): This paper is basically constituted by two parts. In the first part, we consider an interesting conjecture formulated by Elsner (Ann de Inst Fourier 49(1):303-331, 1999) and provide an affirmative answer to it under a very mild assumption. Then, we use the preceding result to provide a detailed characterization of (singular) complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance of these structures stems from several problems involving vector fields with uniform solutions as well as from problems about simultaneous uniformization for leaves of foliations by Riemann surfaces. In this paper, we first describe the local structure of the mentioned projective structures and then go on to derive some global classification building on previous well known material.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24