A note on BV capacities on Grushin spaces

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Abstract

In this paper we formulate some basic properties for the BV capacity and Hausdorff capacity on the Grushin space \(\mathbb {G}^n_{\alpha }\) and develop the sharp BV isocapacity inequalities on \(\mathbb {G}^n_{\alpha }\) under a dimensional condition.

Keywords

Isoperimetric inequality Sub-Riemannian manifolds Grushin spaces BV capacity 

Mathematics Subject Classification

32U20 53C17 

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and TechnologyBeijingPeople’s Republic of China

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