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/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

We study the asymptotics of the number N(t) of geometrically distinct closedgeodesics of a Riemannian or Finsler metric on a connected sum of two compactmanifolds of dimension at least three with non-trivial fundamental groups andapply this result to the prime decomposition of a three-manifold. In particularwe show that the function N(t) grows at least like the prime numbers on acompact 3-manifold with infinite fundamental group. It follows that a genericRiemannian metric on a compact 3-manifold has infinitely many geometricallydistinct closed geodesics. We also consider the case of a connected sum of acompact manifold with positive first Betti number and a simply-connectedmanifold which is not homeomorphic to a sphere.

Closed geodesics on connected sums and 3-manifolds