The geometry of closed surfaces of genus $g\geq 2$ equipped with a Riemannian metric of variable bounded curvature with finitely many conical points is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
"On Riemannian surfaces with conical singularities." Rocky Mountain J. Math. 48 (5) 1455 - 1474, 2018. https://doi.org/10.1216/RMJ-2018-48-5-1455