arXiv subjects

Siddharth Panigrahi

Publications and source records attributed to Siddharth Panigrahi.

2 recordsLinked to original sources

arXiv2025

Decompositions of Scherk-Type Zero Mean Curvature Surfaces

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.

math.DG↗

arXiv2025

Modular Surfaces in Lorentz-Minkowski 3-Space: Curvature and Applications

In this paper, we study the relation of the sign of the Gaussian and mean curvature of modular surfaces in Lorentz-Minkowski $3$-space to the zeroes of the associated complex analytic functions and its derivatives. Further, we completely classify zero Gaussian curvature modular surfaces. Next we show non-existence of non-planar maximal modular surfaces, characterize CMC modular surfaces, analyze asymptotic behaviour of Gaussian curvature of complete modular graphs and the Hessian of their height functions and lastly as application, demonstrate how modular surfaces can be realised as integral surfaces of some conformal field theories and non-linear sigma models.

math.DG↗