Conformal Scalar-flat Metrics With Prescribed Boundary Mean Curvature

2024/10/08 by Shen, Jiashu, Sheng, Hongyi
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.06302

Abstract

Let (M, g) be a compact Riemannian manifold with boundary ∂ M. Given a function f on ∂ M, we consider the problem of finding a conformal metric of g with zero scalar curvature in M and prescribed mean curvature f on ∂ M. Through the construction of local test functions, we resolve most of the remaining open cases from Escobar's work \citearticle15 and establish new solvability conditions.

Related

• A prescribed scalar and boundary mean curvature problem on compact manifolds with boundary
• Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
• Conformal scalar curvature rigidity on Riemannian manifolds
• Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds
• Conformal metrics with prescribed scalar and mean curvature