Metrics of positive curvature with conic singularities on the sphere
A. Eremenko
Abstract
A simple proof is given of the necessary and sufficient condition on a triple of positive numbers A,B,C for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles A,B,C. The same condition is necessary and sufficient for the triple A,B,C to be interior angles of a spherical triangular membrane.
Create a lesson
Related papers
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
Affine dual Minkowski problem for general measures
Cheng Zhang, Hailin Jin
Algebraically independent distances and rigid metrics
Yoshito Ishiki
On the Geometry of Wasserstein Barycenter II: Riemannian Rigidity, Essential Non-Branching, and Finsler Models
Bang-Xian Han, Deng-Yu Liu
A Weak Topology on Metric Spaces
Armando W. Gutiérrez, Olavi Nevanlinna
Uncentered Blaschke-Santaló inequalities for the Gaussian measure
S. Artstein-Avidan, M. Fradelizi, K. Wyczesany