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

The Minkowski function is a crucial tool used in the study of balanceddomains and, more generally, quasi-balanced domains in several complexvariables. If a quasi-balanced domain is bounded and pseudoconvex then it iswell-known that its Minkowski function is plurisubharmonic. In this short note,we prove that under the additional assumption of smoothness of the boundary,the Minkowski function of a quasi-balanced domain is in fact smooth away fromthe origin. This allows us to construct a smooth plurisubharmonic definingfunction for such domains. Our result is new even in the case of balanceddomains.

A note on the smoothness of the Minkowski function