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 Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The dual Minkowski problem for even data asks what are the necessary andsufficient conditions on an even prescribed measure on the unit sphere for itto be the $q$-th dual curvature measure of an origin-symmetric convex body in$\mathbb{R}^n$. A full solution to this is given when $1 < q < n$.  The necessary and sufficient condition is an explicit measure concentrationcondition. A variational approach is used, where the functional is the sum of adual quermassintegral and an entropy integral. The proof requires two crucialestimates. The first is an estimate of the entropy integral proved using aspherical partition. The second is a sharp estimate of the dualquermassintegrals for a carefully chosen barrier convex body.

The dual Minkowski problem for symmetric convex bodies