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

Given a smooth compact manifold with boundary, we study variationalproperties of the volume functional and of the area functional of the boundary,restricted to the space of the Riemannian metrics with prescribed curvature. Weobtain a sufficient and necessary condition for a metric to be a criticalpoint. As a by-product, a very natural analogue of V-statics metrics isobtained. In the second part, using the Yamabe invariant in the boundarysetting, we solve the Kazdan-Warner-Kobayashi problem in a compact manifoldwith boundary. For several cases, depending on the signal of the Yamabeinvariant, we give sufficient and necessary condition for a smooth function tobe the scalar or mean curvature of a metric with constraint on the volume orarea of the boundary.

Critical metrics and curvature of metrics with unit volume or unit area of the boundary