Title: Bj\"{o}rling problems for surfaces in the subspaces of the four-dimensional Lorentz-Minkowski space $\mathbb{L}^4$
Abstract: Bj\"{o}rling problem for minimal surfaces in the Euclidean three-space asks if, given a curve $\gamma$ and a unit vector field $N$ perpendicular to $\gamma$, there exist a minimal surface which contanins $\gamma$ and whose unit normal along $\gamma$ is $N$. This problem was posed and solved by Emanuel Gabriel Bj\"{o}rling in 1844.
Recently there have been many interesting results related to this problem. In particular, this problem can be asked for a variety of surfaces in the subspaces of the four-dimensional Lorentz-Minkowski space $\mathbb{L}^4$ and we review them in this talk.