Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature

Details Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature

2008-06-30

arxiv.org/abs/0806.4885v1

Mathematics

Differential Geometry

26 pages

Scientific paper

We prove nonexistence of nonconstant local minimizers for a class of functionals, which typically appears in the scalar two-phase field model, over a smooth N-dimensional Riemannian manifold without boundary with non-negative Ricci curvature. Conversely for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative we prove existence of nonconstant local minimizers for the same class of functionals.

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