2016/01/19 by Demetre Kazaras, Kazaras, Demetre
Mathematics · #53A10 #53A30 #53C21 #57R65 #58J32 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1601.05169
openalex publication_date 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a gluing theorem for solutions of a Yamabe problem for manifolds\nwith boundary studied by Escobar in the 90's. Given two scalar-flat Riemannian\nmanifolds whose boundary has zero mean curvature and sharing a submanifold K,\nwe produce the generalized connected sum along K. On this third manifold we\nproduce a family of scalar-flat metrics with small, constant mean curvature on\nthe boundary which are close to the original metrics in the C2 sense. Under\nextra geometric conditions on the original manifolds, we can arrange for this\nfamily to also have vanishing mean curvature on the boundary.\n