Local quasi-isometries and tangent cones of definable germs
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Nhan Nguyen
Abstract
In this paper, we introduce the notion of local quasi-isometry for metric germs and prove that two definable germs are quasi-isometric if and only if their tangent cones are bi-Lipschitz homeomorphic. Since bi-Lipschitz equivalence is a particular case of local quasi-isometric equivalence, we obtain Sampaio’s tangent cone theorem as a corollary. As an application, we provide a different proof of the theorem by Fernandes-Sampaio, which states that the tangent cone of a Lipschitz normally embedded germ is also Lipschitz normally embedded.
Acknowledgements
We would like to thank the anonymous referees for their careful reading and valuable suggestions.
Communicated by: D. Plaumann
References
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Articles in the same Issue
- Frontmatter
- Local quasi-isometries and tangent cones of definable germs
- On trialities and their absolute geometries
- An isomorphism between unitals and between related classical groups
- Betweenness isomorphisms in the plane — the case of a circle and points
- Compact locally homogeneous manifolds with parallel Weyl tensor
- Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving
- Equiangular lines in ℂ3
- Vanishing theorems for Mather–Jacobian multiplier ideals on a Gorenstein projective variety
- Deformations of pairs of codimension one foliations
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Articles in the same Issue
- Frontmatter
- Local quasi-isometries and tangent cones of definable germs
- On trialities and their absolute geometries
- An isomorphism between unitals and between related classical groups
- Betweenness isomorphisms in the plane — the case of a circle and points
- Compact locally homogeneous manifolds with parallel Weyl tensor
- Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving
- Equiangular lines in ℂ3
- Vanishing theorems for Mather–Jacobian multiplier ideals on a Gorenstein projective variety
- Deformations of pairs of codimension one foliations
- Arithmetic counts of tropical plane curves and their properties
- Convex Fujita numbers are not determined by the fundamental group
