English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $(M,g)$ be a complete non-compact Riemannian manifold together with afunction $e^h$, which weights the Hausdorff measures associated to theRiemannian metric. In this work we assume lower or upper radial bounds on someweighted or unweighted curvatures of $M$ to deduce comparisons for the weightedisoperimetric quotient and the weighted capacity of metric balls in $M$centered at a point $o\in M$. As a consequence, we obtain parabolicity andhyperbolicity criteria for weighted manifolds generalizing previous ones. Abasic tool in our study is the analysis of the weighted Laplacian of thedistance function from $o$. The technique extends to non-compact submanifoldsproperly immersed in $M$ under certain control on their weighted meancurvature.

Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds