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Journal of the London Mathematical Society 1991 s2-43(3):567-576; doi:10.1112/jlms/s2-43.3.567
© 1991 by London Mathematical Society
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© Oxford University Press

Convexity and the Hemisphere

Wilfrid S. Kendall

Department of Statistics, University of Warwick Coventry CV4 7AL e-mail w.s.kendall{at}cu.warwick.ac.uk

An explicit construction is given of continuous bounded non-negative convex functions which are defined on the product of a small hemisphere with itself and which vanish precisely on the diagonal. It is shown that no such function exists for the strict hemisphere, even if the boundedness requirement is lifted. The generalization to regular geodesic balls is indicated.


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