boundary of star-shaped domain in spherical coordinates

by Medo   Last Updated January 12, 2018 20:20 PM

Let $\Omega\subset \mathbb{R}^{n}$ be a bounded domain that contain the origin and, is star-shaped with respect to the origin too. Is it true that, in spherical coordinates, $\partial \Omega$ is given by $r=r(\omega)$ so that $r$ is a function of the angle only? A reference or proof would be appreciated.

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