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Integral estimates for energy densities of non-constant harmonic maps

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Abstract

Integral estimates of energy densities of non-constant harmonic maps are proved. One of the estimates is used to obtain a lower bound of the Dirichlet energy of non null-homotopic maps from two dimensional manifolds with positive Euler characteristics. An application to the regularity theory of energy minimizing maps is also given.

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  1. Department of Mathematical and System Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu, 432-8561, Japan

    Tôru Nakajima

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  1. Tôru Nakajima
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Correspondence to Tôru Nakajima.

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Dedicated to the memory of Kyûya Masuda.

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Nakajima, T. Integral estimates for energy densities of non-constant harmonic maps. manuscripta math. 160, 327–337 (2019). https://doi.org/10.1007/s00229-019-01121-0

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  • DOI: https://doi.org/10.1007/s00229-019-01121-0

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