Articles written in Proceedings – Mathematical Sciences
Volume 111 Issue 4 November 2001 pp 407-414
Given a smooth function
Volume 113 Issue 2 May 2003 pp 189-193
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surface which give the Weierstrass-Enneper representation. From this we derive the hodographic coordinate ρ
Volume 113 Issue 3 August 2003 pp 353-353 Erratum
Volume 114 Issue 2 May 2004 pp 141-151
Volume 114 Issue 2 May 2004 pp 215-215 Erratum
Volume 121 Issue 1 February 2011 pp 27-35
In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen’s determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrized by $\Psi_0$, a section of a certain bundle. The equivalence of these prequantum bundles are discussed.
Volume 123 Issue 1 February 2013 pp 55-65
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.
Volume 126 Issue 3 August 2016 pp 421-431 Research Article
Using Ramanujan’s identities and the Weierstrass--Enneper representation of minimal surfaces, and the analogue for Born--Infeld solitons, we derive further nontrivial identities