9 citations · 52 across the 14 of their papers we have counts for
15 papers
Special cases of the discretization principle via permutability
Joseph Cho, Mason Pember, Wayne Rossman
We show how permutability of transforms of smooth surfaces with particular characteristics leads to discrete surfaces with discrete analogues of the same characteristics.
Conformal geometry of quasi-umbilical timelike surfaces
Emilio Musso, Lorenzo Nicolodi, Mason Pember
The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the -Einstein universe, the conformal compactification of Minkowski 3-space reali…
Symmetry breaking in geometry
Andreas Fuchs, Udo Hertrich-Jeromin, Mason Pember
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in…
Discrete Weierstrass-type representations
Mason Pember, Denis Polly, Masashi Yasumoto
Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete We…
Channel linear Weingarten surfaces in space forms
Udo Hertrich-Jeromin, Mason Pember, Denis Polly
Channel linear Weingarten surfaces in space forms are investigated in a Lie sphere geometric setting, which allows for a uniform treatment of different ambient geometries. We show…
Constrained elastic curves and surfaces with spherical curvature lines
Joseph Cho, Mason Pember, Gudrun Szewieczek
In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be gener…
Discrete -nets and Guichard nets via discrete Koenigs nets
F. E. Burstall, J. Cho, U. Hertrich-Jeromin +2
We provide a convincing discretisation of Demoulin's -surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
Lie applicable surfaces and curved flats
Francis Burstall, Mason Pember
We investigate curved flats in Lie sphere geometry. We show that in this setting curved flats are in one-to-one correspondence with pairs of Demoulin families of Lie applicable sur…
Quartic differentials and harmonic maps in conformal surface geometry
Francis Burstall, Emilio Musso, Mason Pember
We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the or…
Weierstrass-type representations
Mason Pember
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of t…
G-Deformations of maps into projective space
Mason Pember
-deformability of maps into projective space is characterised by the existence of certain Lie algebra valued 1-forms. This characterisation gives a unified way to obtain well kn…
Channel surfaces in Lie sphere geometry
Mason Pember, Gudrun Szewieczek
We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain -surfaces. Since -surfaces possess a rich transformation theory, we…
Polynomial Conserved Quantities of Lie Applicable Surfaces
Francis E. Burstall, Udo Hertrich-Jeromin, Mason Pember +1
Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic…
Characterizing singularities of a surface in Lie sphere geometry
Mason Pember, Wayne Rossman, Kentaro Saji +1
The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie s…
Lie applicable surfaces
Mason Pember
We give a detailed account of the gauge-theoretic approach to Lie applicable surfaces and the resulting transformation theory. In particular, we show that this approach coincides w…