arXiv subjects

Heayong Shin

Publications and source records attributed to Heayong Shin.

3 recordsLinked to original sources

arXiv2013

Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics

Space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski3-space are both characterized as zero mean curvature surfaces. We are interested in the case where the zero mean curvature surface changes type from space-like to time-like at a given non-degenerate null curve. We consider this phenomenon and its interesting connection to 2-dimensional fluid mechanics in this expository article.

math.DG↗

arXiv2013

Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R^3_1 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across the light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in R^{n+1}_1 that change type across an (n-1)-dimensional light-like plane.

math.DG↗

arXiv2009

Ruled minimal surfaces in the three dimensional Heisenberg group

It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three dimensional Heisenberg group whose mean curvature is zero with respect to both of the standard Riemannian metric and the standard Lorentzian metric.

math.DG↗