A survey is given of the Weierstrass representations of surfaces in three-and four-
dimensional spaces, their applications to the theory of the Willmore functional, and related …

We present a formulation of Willmore flow for triangulated surfaces that permits
extraordinarily large time steps and naturally preserves the quality of the input mesh. The …

Overview In computer graphics applications, quaternions are used to represent three-
dimensional rotations. They provide some key advantages over the traditional way of …

This paper aims to set an account of the left eigenvalue problems for real quaternionic
(finite) matrices. In particular, we will present the Geršgorin type theorems for the left (and …

Let H m× n be the set of all m× n matrices over the real quaternion algebra H={c 0+ c 1 i+ c 2
j+ c 3 k∣ i 2= j 2= k 2= ijk=− 1, c 0, c 1, c 2, c 3∈ R}. A∈ H n× n is known to be η-Hermitian if …

Motivation The shape of a cell is tightly controlled, and reflects important processes
including actomyosin activity, adhesion properties, cell differentiation, and polarization …

Research in differential geometry requires a broad core of knowledge. For over half a
century, this core has begun with the study of curves and surfaces in Euclidean space and …

In this paper a necessary and sufficient condition is established for the existence of the
reflexive re-nonnegative definite solution to the quaternion matrix equation AX A∗= B …

В этой работе мы даем обзор некоторых результатов и проблем, относящихся к
глобальным представлениям поверхностей в трех-и четырехмерных пространствах в …

Spectral mesh analysis and processing methods, namely ones that utilize eigenvalues and
eigenfunctions of linear operators on meshes, have been applied to numerous geometric …