Abstract
We study the extremal problem for weighted combined energy between two concentric annuli and obtain that the extremal mapping is a certain radial mapping. This extends the result obtained by Kalaj (J. Differential Equations, 268(2020)) to a non-Euclidean version. Meanwhile, we get a \(\frac{1}{|w|^{2}}\)-Nitsche type inequality, which generalizes the result in Arch. Math., 107(2016). Furthermore, based on the relationship between weighted combined energy and weighted combined distortion, we also consider the extremal problem for weighted combined distortion on annuli.
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The authors would like to thank the referee for a very careful reading of the manuscript.
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Research supported by the National Natural Science Foundation of China (Grant No.11701459 ).
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Yang, Y., Tang, R. & Feng, X. The extremal problem for weighted combined energy. Arch. Math. 122, 189–202 (2024). https://doi.org/10.1007/s00013-023-01940-4
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DOI: https://doi.org/10.1007/s00013-023-01940-4