Conformal deformation of metrics on subdomains of surfaces (Q1904558)

The paper deals with the prescribing Gaussian curvature problem on subdomain of a surface. Using a variant of a distribution of mass principle to smooth a subdomain of a Riemannian manifold, the authors prove that for critical and supercritical cases, a function can be the Gaussian curvature of some positive conformal metric, provided it satisfies certain conditions.