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, Volume 75, Issue 1, pp 49–63 | Cite as

The equator map and the negative exponential functional

  • Min-Chun Hong
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Abstract

We define a negative exponential harmonic map from the ballB n of ℝn into the sphereS n of ℝ n+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.

Keywords

Weak Solution Riemannian Manifold Unit Ball Energy Density Nonlinear Elliptic System 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Min-Chun Hong
    • 1
  1. 1.Mathematics SepartmentZhejiang UniversityHangzhouP. R. China

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