A rigidity Theorem and a Stability Theorem for two-step nilpotent Lie groups
Vol. 19 (2012), No. 3, Page 281--307.
Baklouti, Ali; ElAloui, Nasreddine;K\'edim, Imed
A rigidity Theorem and a Stability Theorem for two-step nilpotent Lie groups
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Abstract:
Let G be a Lie group and H a connected Lie subgroup of G. Given any discontinuous subgroup Γ for the homogeneous space X=G/H and any deformation of Γ, the deformed discrete subgroup may fail to be discontinuous for X. To understand this phenomenon in the case when G is a two-step nilpotent Lie group, we provide a stratification of the deformation space of the action of Γ on X, which depends upon the dimensions of G−adjoint orbits. As a direct consequence, a rigidity Theorem is given and a certain sufficient condition for the stability property is derived. We also discuss the Hausdorff property of the associated deformation space.
Keywords: Partial differential equations, Sobolev spaces, stratified fluid, inner waves, essential spectrum
Mathematics Subject Classification (2010): Primary 22E25; Secondary 22G15.
Received: 2011-12-02
