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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


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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