Decompositions of Scherk-Type Zero Mean Curvature Surfaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913911882645504 |
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| author | Paul, Subham Vasu, Priyank Panigrahi, Siddharth Singh, Rahul Kumar |
| author_facet | Paul, Subham Vasu, Priyank Panigrahi, Siddharth Singh, Rahul Kumar |
| contents | In this paper, by using a special Euler-Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in Lorentz-Minkowski $3$-space $\mathbb E_1^3$, namely Scherk-type zero mean curvature surfaces, can be expressed as an infinite superposition of dilated helicoids. Further, we also obtain different finite decompositions for these surfaces. We end this paper with an application of these decompositions to formulate maximal codimension 2 surfaces into finite and infinite "sums" of weakly untrapped and *-surfaces in Lorentz-Minkowski 4-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decompositions of Scherk-Type Zero Mean Curvature Surfaces Paul, Subham Vasu, Priyank Panigrahi, Siddharth Singh, Rahul Kumar Differential Geometry In this paper, by using a special Euler-Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in Lorentz-Minkowski $3$-space $\mathbb E_1^3$, namely Scherk-type zero mean curvature surfaces, can be expressed as an infinite superposition of dilated helicoids. Further, we also obtain different finite decompositions for these surfaces. We end this paper with an application of these decompositions to formulate maximal codimension 2 surfaces into finite and infinite "sums" of weakly untrapped and *-surfaces in Lorentz-Minkowski 4-space. |
| title | Decompositions of Scherk-Type Zero Mean Curvature Surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.20166 |