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 Plus

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

Zendy Tools

Zendy Open

We show that for an arbitrarily given closed Riemannian manifold $M$admitting a point $p \in M$ with a single cut point, every closed Riemannianmanifold $N$ admitting a point $q \in N$ with a single cut point isdiffeomorphic to $M$ if the radial curvatures of $N$ at $q$ are sufficientlyclose in the sense of $L^1$-norm to those of $M$ at $p$. Our result hence notonly produces a weak version of the Cartan--Ambrose--Hicks theorem in the casewhere underlying manifolds admit a point with a single cut point, but also is akind of a weak version of the Blaschke conjecture for spheres proved by Berger.In particular that result generalizes one of theorems in Cheeger's Ph.D. Thesisin that case. Remark that every exotic sphere of dimension $> 4$ admits ametric such that there is a point whose cut locus consists of a single point.

Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones