A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$

Alexandre Lymberopoulos; Antonio de Padua Franco Filho; Anuar Enrique Paternina Montalvo

paper

A Cauchy problem for minimal spacelike surfaces in $R_{2}^{4}$

arXiv:1905.08629

Abstract

We give a definition of isoclinic parametric surfaces in $R_{2}^{4}$ and prove that such an isoclinic conformal immersion comes from two holomorphic functions. A Cauchy problem was proposed and solved, namely: construct an isoclinic and minimal positive (negative) spacelike surface in $R_{2}^{4}$ , containing a given positive (negative) real analytic curve. At last, we study the important and well-known Björling problem, providing some examples was given in the last section.

24 pages

A Cauchy problem for minimal spacelike surfaces in R24​

Abstract

A Cauchy problem for minimal spacelike surfaces in $R_{2}^{4}$