Prescribing almost constant scalar curvature and almost constant boundary mean curvature on B^n - Pu, Yixing (Topological Methods in Nonlinear Analysis, 2025)
In this paper, we investigate a boundary case of the classical prescribed curvature problem. We focus on a prescribing scalar curvature which is equal to a given function K and a boundary mean curvature which is equal to a given function H on the standard ball (B^n,g). Our analysis extends previous studies by considering the scenario where the curvatures K and H are close to constants K_0> 0 and H_0> 0. Using a perturbative approach and leveraging the ansatz introduced by Han-Li HanLi_2000, we establish new existence results for the conformal metric when the prescribed curvatures are near constants.