7 citations · 26 across the 17 of their papers we have counts for
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On constant mean curvature surfaces in the Heisenberg group
Dmitry Berdinsky
We study constant mean curvature surfaces in the three-dimensional Heisenberg group. We prove that a constant mean curvature surface in a neighborhood of non-umbilic point is descr…
Willmore-like functionals for surfaces in 3-dimensional Thurston geometries
Dmitry Berdinsky, Yuri Vyatkin
We find analogues of the Willmore functional for each of the Thurston geometries with 4-dimensional isometry group such that the CMC-spheres in these geometries are critical points…
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…
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…