Every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence Riemannian manifolds
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-017-4543-x
Abstract: In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds. read more here.
Keywords: gromov hausdorff; hausdorff limit; manifold gromov; every sub ... See more keywords
Non-embedding theorems of nilpotent Lie groups and sub-Riemannian manifolds
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DOI: 10.1007/s11464-020-0823-3
Abstract: We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD (0, N ) with… read more here.
Keywords: nilpotent lie; non embedding; lie groups; embedding theorems ... See more keywords
Homogenization for sub-riemannian Lagrangians
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DOI: 10.1088/1361-6544/accdae
Abstract: We consider Lagrangians that are defined only on the horizontal distribution of a sub-riemannian manifold. The associated Hamiltonian is neither strictly convex nor coercive. We prove a result on homogenization of the Hamilton–Jacobi equation following… read more here.
Keywords: homogenization sub; riemannian lagrangians; sub riemannian; result ... See more keywords
C-R Immersions and Sub-Riemannian Geometry
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DOI: 10.3390/axioms12040329
Abstract: On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form θ, we consider natural ϵ-contractions, i.e., contractions gϵM of the Levi form Gθ, such that the norm… read more here.
Keywords: immersion; geometry; sub riemannian; riemannian geometry ... See more keywords
Analysis of (sub-)Riemannian PDE-G-CNNs
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DOI: 10.48550/arxiv.2210.00935
Abstract: Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should have been… read more here.
Keywords: sub riemannian; network; pde cnns; cnns ... See more keywords