Journal of Convex Analysis 16 (2009), No. 2, 515--521
Copyright Heldermann Verlag 2009
Peak Set Crossing all the Circles
Piotr Kot
Politechnika Krakowska, Instytut Matematyki, ul. Warszawska 24, 31-155 Kraków, Poland
pkot@pk.edu.pl
[Abstract-pdf]
Let $\Omega\subset\Bbb C^{d}$ be a circular, bounded, strictly convex domain with $C^{2}$ boundary. We construct a peak set $K\subset\partial\Omega$ which intersects all the circles in $\partial\Omega$ with the center at zero. In particular Hausdorff dimension of $K$ is at least $2d-2$.
Keywords: Homogeneous polynomials, peak set, maximum modulus set, inner function.
MSC: 32A05; 32A35
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