Undistorted fillings in subsets of metric spaces
DOKPE
Published in:
 Advances in Mathematics.  2023, vol. 423, no. 109024
English
Lipschitz kconnectivity, Euclidean isoperimetric inequalities, and coning inequalities all measure the difficulty of filling a kdimensional cycle in a space by a (k+1)dimensional object. In many cases, such as Banach spaces and CAT(0) spaces, it is easy to prove Lipschitz connectivity or a coning inequality, but harder to obtain a Euclidean isoperimetric inequality. We show that in spaces of finite Nagata dimension, Lipschitz connectedness implies Euclidean isoperimetric inequalities, and Euclidean isoperimetric inequalities imply coning inequalities. We show this by proving that if X has finite Nagata dimension and is Lipschitz kconnected or admits Euclidean isoperimetric inequalities up to dimension k then any isometric embedding of X into a metric space is isoperimetrically undistorted up to dimension k+1. Since X embeds in L∞, which admits a Euclidean isoperimetric inequality and a coning inequality, X admits such inequalities as well. In addition, we prove that an analog of the FedererFleming deformation theorem holds in such spaces X and use it to show that if X has finite Nagata dimension and is Lipschitz kconnected, then integral (k+1)currents in X can be approximated by Lipschitz chains in total mass.

Faculty
 Faculté des sciences et de médecine

Department
 Département de Mathématiques

Language


Classification

Mathematics

License

License undefined

Open access status

green

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Persistent URL

https://folia.unifr.ch/unifr/documents/324701
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