Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms

Abstract

In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms. In particular, we discuss singularities of discrete surfaces with non-zero constant Gaussian curvature, and parallel surfaces of discrete minimal and maximal surfaces, and discrete constant mean curvature $1$ surfaces in de Sitter $3$-space, including comparisons with different previously known definitions of such singularities.

23 pages

References in corpus (1)

• Discrete constant mean curvature surfaces via conserved quantities

Cited by in corpus (1)

• Semi-discrete linear Weingarten surfaces with Weierstrass-type representations and their singularities