We show that any stable exponentially harmonic map from a compact Riemannian manifold into a compact simply-connected δ-pinched Riemannian manifold under certain circumstance is constant in two different versions. We also prove that a non-constant exponentially harmonic map from a compact hypersurface into a compact Riemannian manifold satisfying certain condition is unstable.

中文翻译：

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指数谐波映射的稳定性

我们证明了任何从紧凑黎曼流形到紧凑简单连接的稳定指数调和映射δ-pinch 黎曼流形在某些情况下在两个不同的版本中是恒定的。我们还证明了从紧凑超曲面到满足特定条件的紧凑黎曼流形的非恒定指数调和映射是不稳定的。