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The equator map and the negative exponential functional

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Abstract

We define a negative exponential harmonic map from the ballB n of ℝn into the sphereS n of ℝn+1. We prove that the equator map\(u^* = (\frac{x}{{\left| x \right|}},0)\) is a negative exponential harmonic map, but not stable for the negative exponential functional whenn≥2. Moreover, we consider maps from a ballB n into the unit sphereS m of ℝm+1 wherem≥2, and prove that no nonconstant, non surjective map can reach either the minimum or the maximum of the negative exponential functional.

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  1. Min-Chun Hong

    Present address: Mathematics Section, International Centre for Theoretical Physics, P. O. Box 586, 34100, Trieste, Italy

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  1. Mathematics Separtment, Zhejiang University, Hangzhou, P. R. China

    Min-Chun Hong

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  1. Min-Chun Hong
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Hong, MC. The equator map and the negative exponential functional. Manuscripta Math 75, 49–63 (1992). https://doi.org/10.1007/BF02567071

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  • DOI: https://doi.org/10.1007/BF02567071

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