Instability of Elliptic Equations on Compact Riemannian Manifolds with Non-negative Ricci Curvature
نویسندگان
چکیده
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 nonnegative 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.
منابع مشابه
Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature
We prove nonexistence of nonconstant local minimizers for a class of functionals, which typically appears in the scalar two-phase field model, over a smoothN−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 ...
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