Nonexistence of stable F-stationary maps of a functional related to pullback metrics

Abstract

Abstract Let M m $M^{m}$ be a compact convex hypersurface in R m + 1 $R^{m+1}$ . In this paper, we prove that if the principal curvatures λ i $\lambda_{i}$ of M m $M^{m}$ satisfy 0 < λ 1 ≤ ⋯ ≤ λ m $0<\lambda_{1}\leq \cdots \leq \lambda_{m}$ and 3 λ m < ∑ j = 1 m − 1 λ j $3\lambda_{m}<\sum_{j=1}^{m-1}\lambda_{j}$ , then there exists no nonconstant stable F-stationary map between M and a compact Riemannian manifold when (6) or (7) holds.

Keywords

• F-stationary map
• compact convex hypersurfaces