Abstract
In this paper, we establish a sharp inequality of the gradient of energy density. We use it in studying stability of domain and pinching of energy. And we get the sharp conclusion respectly. In addition, we connect the existence of non-constant totally geodesic maps with the construction of manifolds on topology and geometry.
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Youning, W. The stability of domain and the pinching of energy about harmonic maps. Acta Mathematica Sinica 6, 57–64 (1990). https://doi.org/10.1007/BF02108864
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DOI: https://doi.org/10.1007/BF02108864