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, Volume 160, Issue 3–4, pp 327–337 | Cite as

Integral estimates for energy densities of non-constant harmonic maps

  • Tôru NakajimaEmail author


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.

Mathematics Subject Classification

35A15 53C43 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical and System Engineering, Faculty of EngineeringShizuoka UniversityHamamatsuJapan

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