Displaying similar documents to “Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds”

Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups

Rory Biggs (2017)

Communications in Mathematics

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We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry...

Besov spaces and function series on Lie groups (II).

Leszek Skrzypczak (1993)

Collectanea Mathematica

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In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups. [Part I of the article in MR1240211].

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovski (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.

Curvature and the equivalence problem in sub-Riemannian geometry

Erlend Grong (2022)

Archivum Mathematicum

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These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples,...