Uniqueness of Positive Solutions of the Conformal Scalar Curvature Equation and Applications to Conformal Transformations

1996/10/25 by Man Chun Leung, Leung, Man Chun
Mathematics · #35J60 (Primary) 58G03 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #dg-ga #math.DG #msc:35J60 #msc:58G03

paper · pdf · doi:10.48550/arxiv.dg-ga/9610014

LaTeX, 16 pages

arxiv created 1996/10/25 · openalex publication_date 1996/10/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete Riemannian manifolds of constant negative scalar curvature are isometries. We also study uniqueness of complete positive solutions and radial solutions.

Citations

• Conformal Deformation of Warped Products and Scalar Curvature Functions on Open Manifolds

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