arXiv subjects

Shuki Sano

Publications and source records attributed to Shuki Sano.

2 recordsLinked to original sources

arXiv2026

Approximation and Interpolation Theorems for Maximal Surfaces with Singularities

In this paper, we prove an approximation and interpolation theorem for maxfaces in the Lorentz--Minkowski $3$-space $\mathbb{L}^3$. Alarc\'on, Forstneri\v{c}, and L\'opez established approximation and interpolation theorems for conformal minimal surfaces using the Enneper--Weierstrass representation formula. We survey their methods and apply them to maxfaces. Furthermore, by incorporating singularity criteria based on the Weierstrass data of maxfaces into the approximation and interpolation theorem, we demonstrate the existence of a maxface with prescribed singularities at specified points, as well as the existence of a maxface whose singular set has a dense image in $\mathbb{L}^3$.

math.DG↗

arXiv2026

Criteria and Curvatures for Singularities of Finite Multiplicities of Curves in $\boldsymbol{R}^N$

First, this paper presents a systematic procedure for constructing criteria for singularities of curves of finite multiplicities in $\boldsymbol{R}^N$. Based on this method, we provide explicit criteria for singularities of multiplicities two, three, and four, including specific cusps appearing only in dimensions three or higher. Furthermore, we generalize the normalized curvature functions and the cuspidal curvature to singular curves in $\boldsymbol{R}^N$. Using these generalized curvatures, we reinterpret the existence and uniqueness theorem given by Fukui for curves in $\boldsymbol{R}^N$ of finite multiplicities.

math.DG↗