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

Conformal qc geometry of spherical qc manifolds are investigated. Weconstruct the qc Yamabe operators on qc manifolds, which are covariant underthe conformal qc transformations. A qc manifold is scalar positive, negative orvanishing if and only if its qc Yamabe invariant is positive, negative or zero,respectively. On a scalar positive spherical qc manifold, we can construct theGreen function of the qc Yamabe operator, which can be applied to construct aconformally invariant tensor. It becomes a spherical qc metric if the qcpositive mass conjecture is true. Conformal qc geometry of spherical qcmanifolds can be applied to study convex cocompact subgroups of ${\rmSp}(n+1,1).$ On a spherical qc manifold constructed from such a discretesubgroup, we construct a spherical qc metric of Nayatani type. As a corollary,we prove that such a spherical qc manifold is scalar positive, negative orvanishing if and only if the Poincar\'e critical exponent of the discretesubgroup is less than, greater than or equal to $2n+2$, respectively.

On Conformal Qc Geometry, Spherical Qc Manifolds and Convex Cocompact Subgroups of ${\rm Sp}{(n+1,1)}$