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Boundary extensions for mappings between metric spaces

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In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable Jacobian determinant and mappings of exponentially integrable distortion with integrable Jacobian determinant. Our main results extend the corresponding results of Äkkinen and Guo (Ann. Mat. Pure. Appl. 2017) to the setting of metric measure spaces.

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Notes

  1. We recommend the readers to the monograph [16] for more information.

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Acknowledgements

The authors would like to thank Prof. Chang-Yu Guo for posing this question and for many useful conservations. They also thank Lin Cao, Yu-Heng Lan and Li-Jie Fang for many useful conservations. Last but not least, they are grateful to the referees for their helpful comments.

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Authors and Affiliations

  1. Center for Optics Research and Engineering, Shandong University, Qingdao, 266237, People’s Republic of China

    Yao-Lan Tian

  2. Research Center for Mathematics, Shandong University, Qingdao, 266237, People’s Republic of China

    Yi Xuan

  3. Frontiers Science Center for Nonlinear Expectations, Ministry of Education, Beijing, People’s Republic of China

    Yi Xuan

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  1. Yao-Lan Tian
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  2. Yi Xuan
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Yao-Lan Tian and Yi Xuan wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Yi Xuan.

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The authors are supported by the Young Scientist Program of the Ministry of Science and Technology of China (No. 2021YFA1002200), the National Natural Science Foundation of China (No. 12101362) and the Natural Science Foundation of Shandong Province (No. ZR2022YQ01 and No. ZR2021QA003).

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Tian, YL., Xuan, Y. Boundary extensions for mappings between metric spaces. Anal.Math.Phys. 14, 49 (2024). https://doi.org/10.1007/s13324-024-00906-1

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