More on the Potential for the Farthest-Point Distance Function

For some particular cases in dimension 3 and higher we prove a conjecture of Laugesen and Pritsker (Canad. Math. Bull., 46 , pp. 373–387, 2003 ) concerning the probability measure related with the farthest-point distance function. In dimension 2 we offer an alternative proof for the result by Gardin...

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Bibliographic Details
Published inPotential analysis Vol. 42; no. 3; pp. 699 - 716
Main Authors Kawohl, Bernd, Nitsch, Carlo, Sweers, Guido
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2015
Subjects
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
52A20
52A40
Farthest-point distance function
Secondary 31B10
Positive measures
Primary 31A15
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Summary:For some particular cases in dimension 3 and higher we prove a conjecture of Laugesen and Pritsker (Canad. Math. Bull., 46 , pp. 373–387, 2003 ) concerning the probability measure related with the farthest-point distance function. In dimension 2 we offer an alternative proof for the result by Gardiner and Netuka. We also consider some examples that may provide more insight in the nature of the problem.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-014-9454-1