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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The volume growth function of a Riemannian manifold of bounded geometry is afunction having bounded growth of derivative, called a bgd-function. Grimaldiand Pansu showed that any one-ended manifold of finite type admits a metric ofbounded geometry such that the volume growth function has the growth type ofany given bgd-function. In the case of infinite type, this holds for anysuperlinear bgd-function. We generalize this result to manifolds with finitelymany ends and show that a manifold with infinitely many ends does not admit ametric with some bgd-functions as volume growth, including polynomials. We alsoprove that on certain manifolds with countably many ends, there exist metricssuch that the volume growth functions have a growth type arbitrarily close tothat of any predetermined bgd-function.

Volume growth on manifolds with more than one end