Born-Infeld Solitons and Existence & Non-uniqueness of Solutions to the Björling Problem

2022/11/07 by Das, Arka
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.03275

Abstract

In this semi-expository article, we study Born-Infeld soliton surfaces as zero mean curvature surfaces and derive conformal parameters for them. Then we present two approaches to solve the Björling problem for such surfaces, one of them treating them as time-like minimal surfaces and the other one using the Barbashov-Chernikov representation. Finally, we show that the solution to the Björling problem may not be unique unlike minimal and maximal surfaces.

Related

• On the Björling problem for Born-Infeld solitons
• Finite Decomposition of Minimal surfaces, Maximal surfaces, Timelike Minimal surfaces and Born-Infeld solitons
• Ramanujan's identities, minimal surfaces and solitons
• The Björling problem for prescribed mean curvature surfaces in ℝ³
• Explicit self-similiar singularity of Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation