• RAHUL KUMAR SINGH

Articles written in Proceedings – Mathematical Sciences

• Wick rotations of solutions to the minimal surface equation, the zero mean curvature equation and the Born–Infeld equation

In this paper, we investigate relations between solutions to the minimal surface equation in Euclidean 3-space $\mathbb{E}^{3}$, the zero mean curvature equation in the Lorentz–Minkowski 3-space $\mathbb{L}^{3}$ and the Born–Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and imaginary solutions after Wick rotations are written by symmetries of solutions, and reveal how real and imaginary solutions are transformed under Wick rotations. We also give a transformation method for zero mean curvature surfaces containing light like lines with some symmetries. As an application, we give new correspondences among some solutions to the above equations by using the non-commutativity between Wick rotations and isometries in the ambient space.

• On Euler–Ramanujan formula, Dirichlet series and minimal surfaces

In this paper, we rewrite two forms of an Euler–Ramanujan identity in terms of certain Dirichlet series and derive functional equation of the latter.We also use the Weierstrass–Enneper representation of minimal surfaces to obtain some identitiesinvolving these Dirichlet series and one complex parameter.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019