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Dmitry A. Berdinsky

Publications and source records attributed to Dmitry A. Berdinsky.

2 recordsLinked to original sources
arXiv2006

Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

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 the Weierstrass representation of surfaces (see math.DG/0503707). By using surfaces of revolution we demonstrate that it resembles the Willmore functional for surfaces in the Euclidean space in many geometrical respects. We also observe the relation of these functionals to the isoperimetric problem.

math.DG↗
arXiv2005

Surfaces in three-dimensional Lie groups

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 equations for minimal surfaces in these groups. By using the spectral properties of the corresponding Dirac operators we find analogs of the Willmore functional for surfaces in these geometries.

math.DG↗