Among metrics of constant positive curvature on a punctured compact Riemann surface with
conical singularities at the punctures, dihedral monodromy means that the action of the …

Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one
and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral …

The topology of the moduli space for Lamé functions of degree m is determined: this is a
Riemann surface which consists of two connected components when m≥ 2; we find the …

We analyse local features of the spaces of representations of the fundamental group of a
punctured surface in $\mathrm {SU} _2 $ equipped with a decoration, namely a choice of a …

We prove that any minimal Lagrangian diffeomorphism between two closed spherical
surfaces with cone singularities is an isometry, without any assumption on the multiangles of …

In this paper, we construct a family of surfaces with constant curvature one, each featuring
two conical singularities, and map them from football metrics into $\mathbb {E}^{3} …

We give a complete characterization of the classical Lam\'e equations $ y''=(n (n+ 1)\wp (z)+
B) y $, $ n\in\Bbb R $, $ B\in\Bbb C $ on flat tori $ E_\tau=\Bbb C/(\Bbb Z+\Bbb Z\,\tau) $ with …

Metrics of constant positive curvature with conic singularities Page 1 Metrics of constant positive
curvature with conic singularities Alexandre Eremenko March 21, 2024 Abstract We consider …

We describe the space of spherical triangles (in the sense of Schwarz and Klein). It is a
smooth connected orientable 3 manifold, homotopy equivalent to the 1-skeleton of the cubic …

A conformal metric ${\rm d} s^{2} $ with finitely many conical singularities of constant
Gaussian curvature $ K= 1$ on a compact Riemann surface is referred to as a spherical …