On surfaces with conical singularities of arbitrary angle

TL;DR

This paper investigates the geometry of closed surfaces with Euclidean metrics featuring conical singularities of any angle, demonstrating that their closed geodesics are densely distributed among all geodesics.

Contribution

It establishes the density of closed geodesics in the space of all geodesics on surfaces with arbitrary conical singularities, extending understanding of their geometric structure.

Findings

Closed geodesics are dense in the space of all geodesics.

Surfaces with arbitrary conical angles exhibit rich geodesic behavior.

The study advances the geometric theory of singular Euclidean surfaces.

Abstract

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.