Abstract
AbstractThis paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes onN-dimensional$$\textrm{RCD}(K,N)$$RCD(K,N)spaces$$(X,\textsf {d},\mathscr {H}^N)$$(X,d,HN). Moreover, we obtain almost regularity theorems formulated in terms of the isoperimetric profile and enhanced consequences at the level of several functional inequalities. Most of our statements seem to be new even in the classical setting of smooth, non compact manifolds with lower Ricci curvature bounds. The synthetic theory plays a key role via compactness and stability arguments.
Publisher
Springer Science and Business Media LLC
Cited by
5 articles.
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