Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional
Copyright policy )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.
21 pages, some typos and references corrected
- Siberian Branch of the Russian Academy of Sciences Russian Federation
- Sobolev Institute of Mathematics Russian Federation
- Department of Mathematical Sciences Russian Federation
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, surface of revolution, Differential Geometry (math.DG), Nilpotent and solvable Lie groups, Spectral problems; spectral geometry; scattering theory on manifolds, isoperimetric problem, FOS: Mathematics, Variational principles in infinite-dimensional spaces, Heisenberg group, Willmore functional
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, surface of revolution, Differential Geometry (math.DG), Nilpotent and solvable Lie groups, Spectral problems; spectral geometry; scattering theory on manifolds, isoperimetric problem, FOS: Mathematics, Variational principles in infinite-dimensional spaces, Heisenberg group, Willmore functional
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