INSTABILITY OF ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS WITH NON-NEGATIVE RICCI CURVATURE

Arnaldo Nascimento, Alexandre Alves
2010 Electronic Journal of Differential Equations   unpublished
We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant local minimizers for the same class of functionals.
fatcat:igd36enarzbzhpqtdkqiwuesui