Prescribing scalar and boundary mean curvature on the three dimensional sphere

2002/11/14 by Zindine Djadli, Djadli, Zindine, Andrea Malchiodi +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J60 #msc:53C21 #msc:58G30

paper · pdf · doi:10.48550/arxiv.math/0211227

arxiv created 2002/11/14 · arxiv updated 2009/11/30

Abstract

We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.

Citations

• Uniqueness theorems through the method of moving spheres
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Global and local behavior of positive solutions of nonlinear elliptic equations

Related

• The Scalar Curvature Problem on the Four Dimensional Half Sphere
• Prescribing curvatures on three dimensional Riemannian manifolds with boundaries
• Prescribing the scalar curvature under minimal boundary conditions on the half sphere
• Conformal metrics with prescribed scalar and mean curvature
• Prescribing almost constant curvatures on manifolds with boundary