Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the Torus

Abstract: In the spirit of the paper "Large conformal metrics of prescribed Gauss curvature on surfaces of higher genus" by Borer-Galimberti-Struwe, where we dealt with the case of a closed Riemann surface $(M,g_0)$ of genus greater than one, here we study the behaviour of the conformal metrics $g_\lambda$ of prescribed Gauss curvature $K_{g_\lambda} = f_0 + \lambda$ on the torus, when the parameter $\lambda$ tends to one of the boundary points of the interval of existence of $g_\lambda$, and we characterize their "bubbling behaviour".