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Superposition of generalized maximal immersions and its applications

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Abstract

We derive a variant of the Weierstrass–Enneper representation for generalized maximal immersions generated by a single harmonic function. We use this variant to construct examples of generalized maximal immersion from a single family. Subsequently, we proved a ‘superposition principle’ for generalized maximal immersions. It says that if we have given finitely many generalized maximal immersions, one can add their parametrizations to get another generalized maximal immersion under certain assumptions. We also study how the singularity of maxfaces behaves under superposition.

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Acknowledgements

The first author would like to acknowledge the External Grant he received, namely UGC-JRF (Beneficiary Code/Flag-BININ01854128 A) sanctioned by the University Grants Commission and the facilities provided by the Department of Mathematics, IIT Patna, to carry out this research. The second author would like to acknowledge the external grant he has obtained, namely MATRICS (File no. MTR/2023/000990). The authors would also like to thank Dr Pradip Kumar, Assistant Professor, Department of Mathematics, Shiv Nadar University, India. His valuable comments enriched the content of this article. The authors also express their deep appreciation to the anonymous referee for his/her invaluable comments, which greatly contributed to the improvement of the article.

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  1. Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna, 801106, India

    Subham Paul & Rahul Kumar Singh

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  1. Subham Paul
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  2. Rahul Kumar Singh
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Correspondence to Subham Paul.

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Communicated by Mahender Singh.

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Paul, S., Singh, R.K. Superposition of generalized maximal immersions and its applications. Proc Math Sci 134, 11 (2024). https://doi.org/10.1007/s12044-024-00780-8

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  • DOI: https://doi.org/10.1007/s12044-024-00780-8

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