Curvature Deformations on Complete Manifolds with Boundary

2025/01/18 by Tiarlos Cruz, Cruz, Tiarlos, Almir Silva Santos +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2501.10855

openalex publication_date 2025/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics with positive scalar curvature and mean convex boundary. Building upon these results, we explore further deformation scenarios, including those that increase the mean curvature. Finally, we consider the case of deforming complete manifolds with negative scalar curvature on manifolds with noncompact boundary.

Related

• Scalar curvature deformations with non-compact boundaries
• Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
• Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• Deformation of the scalar curvature and the mean curvature