Publications

Published/submitted articles

1. (Submitted) With Shiochi Fujimori, Indranil Biswas and Pradip Kumar: Higher genus Angel Surfaces.

Abstract: We prove the existence of complete minimal surfaces in $\mathbb{R}^3$ of arbitrary genus $p\, >\, 1$ and least absolute curvature with precisely two ends --- one catenoidal and one Enneper-type --- thereby resolving, affirmatively, a conjecture posed by Weber. These surfaces, which are called \emph{Angel surfaces}, generalize the genus-one example constructed earlier by Fujimori and Shoda. We extend the orthodisk method developed by Weber and Wolf, \cite{weber2002teichmuller}, to construct the minimal surfaces. A central idea in our construction is the notion of \emph{partial symmetry}, which enables us to introduce controlled symmetry into the surface.

Article link

2. (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.

3. Bardhan, R., Dhochak, A. & Kumar, P. Cuspidal crosscaps and folded singularities on a maxface and a minface. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00414-1, Article link

4. 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.