A priori estimates for the scalar curvature equation on S³

2004/12/02 by Matthias Schneider, Schneider, Matthias
Mathematics · #35J20 #35J60 #55C21 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J20 #msc:35J60 #msc:55C21

paper · pdf · doi:10.48550/arxiv.math/0412047

36 pages

arxiv created 2004/12/02 · openalex publication_date 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a priori estimates for solutions to the prescribed scalar curvature equation on S³. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient for the existence of a priori estimates, when the curvature function is a positive Morse function.

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