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The leitmotif of this dissertation is the search for length formulas and sharp constants in relation with simple closed geodesics on hyperbolic compact Riemann surfaces. The main tools used are those of hyperbolic trigonometry, topological properties of si ...
We study the Berger-Nirenberg problem on surfaces with conical singularities, i.e, we discuss conditions under which a function on a Riemann surface is the Gaussian curvature of some conformal metric with a prescribed set of singularities of conical types. ...
In this article, we study the problem (sometimes called the Berger-Nirenberg problem) of prescribing the curvature on a Riemann surface (that is on an oriented surface equipped with a conformal class of Riemannian metrics). ...
Let S and S′ be compact Riemann surfaces of the same genus g (gge2) endowed with the Poincaré metric of constant negative curvature -1. par The authors show that for every epsilon>0, there exists an integer m=m(g,epsilon) with the property: Assum ...
The authors examine the space of Riemann surfaces of signature (1,1) with metric of curvature -1 and geodesic boundary. They solve explicitly the moduli problem in this case and show furthermore that two surfaces of this type having the same length spectru ...
We study conditions under which a point of a Riemannian surface has a neighborhood that can be parametrized by polar coordinates. The point under investigation can be a regular point or a conical singularity. We also study the regularity of these polar coo ...
In this paper, we prove that if f is a conformal map between two Riemannian surfaces, and if the curvature of the target is nonpositive and less than or equal to the curvature of the source, then the map is contracting. ...
We prove in this paper that evry compact Riemann surface carries an euclidean (flat) conformal metric with precribed conical singularities of given angles, provided the Gauss-Bonnet relation is satisfied. This metric is unique up to homothety. ...
We study the problem of prescribing the curvature on Riemann surfaces. We extend some results that are classical in the compact case to the non compact case. ...
