Prescribing almost constant curvatures on manifolds with boundary

Abstract

In this paper, we investigate a boundary case of the classical prescribed curvature problem. We focus on prescribing the scalar curvature function K and the boundary mean curvature H on the standard ball. Our analysis extendes previous studies by considering the scenario where the curvatures K and H are close to constants. Using a perturbative approach and leveraging the ansatz introduced by Han and Li, we establish new existence results for the conformal metric when the prescribed curvatures are near constants

arXiv commentThe main result in the paper is the same as another one already published in the paper [Ambrosetti, Li, and Andrea Malchiodi, 2002]