A new framework of zero mean curvature surfaces in the isotropic 3-space

Riku Kishida

A new framework of zero mean curvature surfaces in the isotropic 3-space

Differential Geometry 2026-04-27 v1

Authors: Riku Kishida

Abstract

We introduce a class of zero mean curvature surfaces with singularities in the isotropic 3-space, called ZMC-faces. As a main result, we establish three Osserman-type inequalities for a ZMC-face under certain assumptions on both completeness and finiteness of the total curvature. The equality conditions of these inequalities are related to the asymptotic behaviors of the ends. Moreover, we present several examples of ZMC-faces attaining equalities in these inequalities.

Keywords

zero mean curvature isotropic 3-space ZMC-faces Osserman inequality total curvature asymptotic behavior

Cite

@article{arxiv.2604.22698,
  title  = {A new framework of zero mean curvature surfaces in the isotropic 3-space},
  author = {Riku Kishida},
  journal= {arXiv preprint arXiv:2604.22698},
  year   = {2026}
}

Comments

30 pages, 9 figures

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