Isoperimetric inequality for Hausdorff content and some of its applications

Abstract: We will discuss the isoperimetric inequality for Hausdorff content and compact metric spaces in (possibly infinite-dimensional) Banach spaces. We will also discuss some of its implications for systolic geometry, in particular, systolic inequalities of a new type that are true for much wider classes of non-simply connected Riemannian manifolds than Gromov’s classical systolic inequality.

Joint work with Y. Liokumovich, B. Lishak, and R. Rotman.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Topology and geometry: extremal and typical

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