3 papers
math.GR2019
Towards quantitative classification of Cayley automatic groups
Dmitry Berdinsky, Phongpitak Trakuldit
In this paper we address the problem of quantitative classification of Cayley automatic groups in terms of a certain numerical characteristic which we earlier introduced for this c…
math.DG2006
Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional
Dmitry A. Berdinsky, Iskander A. Taimanov
We study the generalization of the Willmore functional for surfaces in the three-Heisenberg group. Its construction is based on the spectral theory of the Dirac operator coming to…
math.DG2005
Surfaces in three-dimensional Lie groups
Dmitry A. Berdinsky, Iskander A. Taimanov
We derive the Weierstrass (or spinor) representation for surfaces in three-dimensional Lie groups Nil, \tilde{SL}_2, and Sol with Thurston's geometries and establish the generating…