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2019•Journal of Topology and AnalysisRequires access

Stability of exponentially harmonic maps

Yuan-Jen Chiang

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Abstract

We show that any stable exponentially harmonic map from a compact Riemannian manifold into a compact simply-connected [Formula: see text]-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.

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What this paper is about

We show that any stable exponentially harmonic map from a compact Riemannian manifold into a compact simply-connected [Formula: see text]-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.

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Available abstract

We show that any stable exponentially harmonic map from a compact Riemannian manifold into a compact simply-connected [Formula: see text]-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.

Key concepts: Mathematics, Riemannian manifold, Harmonic map, Exponential map (Riemannian geometry), Hypersurface, Manifold (fluid mechanics), Exponential growth, Constant (computer programming)

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