4. Variational problems on Riemannian manifolds

Abstract

4.1 Example manifolds and their representations 4.2 Supercritical boundary value problems 4.2.1 A weak substitute for the vector-field x 4.2.2 Critical points of a free functional 4.2.3 Critical points of constrained functionals 4.2.4 Applications 4.3 Harmonic maps 4.4 Supercritical boundary value problems: revisited 4.4.1 A better substitute for the vector-field x? 4.4.2 Conformal vector-fields and conformal maps 4.4.3 Yamabe’s equation 4.4.4 Yamabe’s equation with boundary terms 4.4.5 Conformal vector fields on conformally flat manifolds 4.4.6 The bifurcation problem on \(\mathbb {R}^n\), \(\mathbb {S}^n\), \(\mathbb {H}^n\) 4.4.7 The bifurcation problem on rotation surfaces 4.5 Harmonic maps into conformally flat manifolds