Add to ORKGWe consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function) under the two metrics are the same, then the two metrics are uniformly close. We prove the rigidity theorem for relatively hyperbolic groups. This generalizes a result of Fujiwara.Comment: 16 pages, comments are welcome
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We construct affine uniformly Lipschitz actions on $\ell^1$ and $L^1$ for certain groups with hyperb...
Given a finitely generated group, a natural metric on it, arising just from its algebraic structure,...
AbstractIn this paper we show that if two Zariski dense representations, from a group G into Iso(X) ...
In this thesis, we discuss various rigidity results for geodesic length spaces that are not Riemanni...
The marked length spectrum (MLS) of a closed negatively curved manifold $(M, g)$ is known to determi...
This dissertation explores the extent to which lengths of closed geodesics on a Riemannian manifold ...
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any qua...
This article is the second in a series of two whose aim is to extend a recent result of Guillarmou-L...
AbstractIn this note we show the marked length rigidity of symmetric spaces. More precisely, if X an...
We characterize the Lie groups with finitely many connected components that are $O(u)$-bilipschitz e...
We study the coarse geometry of the mapping class group of a compact orientable surface. We show th...
46 pages, 1 figureWe prove a radial source estimate in H\"older-Zygmund spaces for uniformly hyperbo...
We study the metric and topological properties of the space $\mathscr{D}(G)$ of left-invariant hyper...
In this article, we prove that if two warped cones corresponding to two groups with free, isometric,...
In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two conseque...
We construct affine uniformly Lipschitz actions on $\ell^1$ and $L^1$ for certain groups with hyperb...
Given a finitely generated group, a natural metric on it, arising just from its algebraic structure,...
AbstractIn this paper we show that if two Zariski dense representations, from a group G into Iso(X) ...