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Rivu Bardhan, Indranil Biswas, Pradip Kumar: Higher genus maxfaces with Enneper end, The Journal of Geometric Analysis:, 34, 207 (2024) https://arxiv.org/abs/2310.00235, Journal Link of article.
(Submitted) With Indranil Biswas, Pradip Kumar, Subham Paul: On the Complete maximal maps and their singularities.
Abstract: This article explores the construction of higher genus, complete maximal maps in Lorentz-Minkowski space, as well as relationships between the genus and the number of singular components. In the generic case, it is proved that a non-planar, complete maximal map of genus \(p\) has at least \(p+1\) connected singular components. Furthermore, it is shown that for given \(p\) and \(n \,>\, p+2\), there exists a complete maximal map of genus \(p\) with \(2n\) complete ends and at least \(2n\) components in the non-degenerate singular set. As a corollary, for any \(p\, \geq\, 0\), we can construct a maximal map of genus \(p\) with a large number of singular components.