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We give necessary and sufficient conditions on the singular Björling data such that the singular Björling problem’s solution has a prescribed nature of singularity. As an application, for a given maxface with a particular type of singularity, we find a sequence of maxfaces, all having a cuspidal-edge. © 2022, Springer Nature Switzerland AG.

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Approximating singularities by a cuspidal-edge on a maxface

When a connected component of the set of singular points of the maxface X consists of only generalized cone-like singular point, we construct a sequence of maxfaces Xn, with an increasing number of swallowtails, converging to the maxface X. We include the general discussion toward this. © 2022, Indian Academy of Sciences.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Swallowtails and cone-like singularities on a maxface

We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, L3, using the identification of L3 with C × R. Further we give a different proof for the singular Björling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity. © 2018 International Society for Photogrammetry and Remote Sensing. All Rights Reserved.

Journal of the Ramanujan Mathematical Society

Existence of maximal surface containing given curve and special singularity

Perturbation bounds for Mostow's decomposition and the bipolar decomposition of matrices have been computed. To do so, expressions for the derivative of the geometric mean of two positive definite matrices have been derived. © 2017 Elsevier Inc.

Linear Algebra and Its Applications

Perturbation bounds for Mostow's decomposition and the bipolar decomposition

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, øij)}i, j en, where Mi are modeled over reflexive Banach space and Hx is compatible with the projective system (defined in the article). We associate to each point x M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure. © 2015 World Scientific Publishing Company.

International Journal of Geometric Methods in Modern Physics

Darboux chart on projective limit of weak symplectic Banach manifold

In this paper, we discuss a one parameter family of complex Born-Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B-I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B-I equations is responsible for it. © Indian Academy of Sciences.

One-parameter family of solitons from minimal surfaces

Let M be a complex manifold and let PM C∞([0, 1], M) be space of smooth paths over M. We prove that the induced almost complex structure on PM is weak integrable by extending the result of Indranil Biswas and Saikat Chatterjee of [Geometric structures on path spaces, Int. J. Geom. Meth. Mod. Phys. 8(7) (2011) 1553-1569]. Further we prove that if M is smooth manifold with corner and N is any complex manifold then induced almost complex structure ℑ on Fréchet manifold C∞(M, N) is weak integrable. © 2013 World Scientific Publishing Company.