In this paper, by virtue of unfolding theory in singularity theory, we investigate the
singularities of five special surfaces generated by a regular curve lying on a spacelike …

We study a generalization of constant Gauss curvature-1-1 surfaces in Euclidean 3-space,
based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the …

The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of
dimension 3 is to find the surface which contains a given curve with a prescribed tangent …

Fold singular points play important roles in the theory of maximal surfaces. For example, if a
maximal surface admits fold singular points, it can be extended to a timelike minimal surface …

We give necessary and sufficient conditions on the singular Björling data such that the
singular Björling problem's solution has a prescribed nature of singularity. As an application …

We solve the $ Bj {\ddot {o}} rling $ problem for constant mean curvature one surfaces in
hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular …

Meridian surfaces of elliptic or hyperbolic type in the four-dimensional Minkowski space∗ 1.
Introduction Page 1 MATHEMATICAL COMMUNICATIONS 1 Math. Commun. 21(2016), 1–21 …

We investigate geometric properties of surfaces given by certain formulae. In particular, we
calculate the singular curvature and the limiting normal curvature of such surfaces along the …

We give criteria for singularities of spacelike constant mean curvature surfaces in 3-
dimensional de Sitter and anti-de Sitter spaces constructed by the DPW method, which is a …

We use integrable systems techniques to study the singularities of timelike non-minimal
constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The …