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- W3100033512 abstract "Let $G$ be a group, $(M,d)$ be a metric space, $X$ be a compact subspace of $M$ and $varphi:Gtimes M rightarrow M$ be a left action by homeomorphisms of $G$ on $M$. Denote $gp=f(g,p)$. The isotropy subgroup of $G$ with respect to $X$ is defined by $H_X={gin G; gX=X}$. In this work we define the induced Hausdorff metric on $G/H_X$ by $d_X(gH_X,hH_X)=d_H(gX,hX)$, where $d_H$ is the Hausdorff distance on $M$. Let $hat d_X$ be the intrinsic metric induced by $d_X$. In this work we study the geometry of $(G/H_X,d_X)$ and $(G/H_X,hat d_X)$. In particular, we prove that if $G$ is a Lie group, $M$ is a differentiable manifold endowed with a metric $d$ which is locally Lipschitz equivalent to a Finsler metric, $X$ is a compact subset of $M$ and $varphi:G times M rightarrow M$ is a smooth left action by isometries of $G$ on $M$, then $(G/H_X,hat d_X)$ is $C^0$-Finsler." @default.
- W3100033512 created "2020-11-23" @default.
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- W3100033512 date "2017-03-22" @default.
- W3100033512 modified "2023-10-03" @default.
- W3100033512 title "Induced Hausdorff Metrics on Quotient Spaces" @default.
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- W3100033512 doi "https://doi.org/10.1007/s00574-017-0032-1" @default.
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