A compactness theorem for surfaces with Bounded Integral Curvature

Clément Debin (1)

1 IF - Institut Fourier

We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface Σ. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation of singularities is allowed.

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Clément Debin. A compactness theorem for surfaces with Bounded Integral Curvature. 2016. ⟨hal-01320662v3⟩