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A note on the smoothness of the Minkowski function
Published in Taylor and Francis Ltd.
2021
Volume: 66
   
Issue: 4
Pages: 541 - 545
Abstract
The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain is bounded and pseudoconvex then it is well-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 from the origin. This allows us to construct a smooth plurisubharmonic defining function for such domains. Our result is new even in the case of balanced domains. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
About the journal
JournalData powered by TypesetComplex Variables and Elliptic Equations
PublisherData powered by TypesetTaylor and Francis Ltd.
ISSN17476933