Geodesic
On the Phragmen--Lindelof principle for subharmonic functions
Izvestiya. Mathematics , Tome 63 (1999) no. 2, pp. 401-422.

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We consider subharmonic functions $f(z)$ in a domain $D\subset\mathbb C$ such that $f(z)$ does not exceed some constant $C$ at all points of $\partial D\setminus\zeta$, $\zeta\in\partial D$. Theorems of Phragmen–Lindelof type provide an upper bound (depending on the structure of the domain $D$) for the a priori possible growth of $f(z)$ as $z\to\zeta$ such that functions satisfying this estimate do not exceed $C$ in the whole domain $D$. We obtain a Phragmen–Lindelof type theorem in which the restriction on the possible growth of $f(z)$ as $z\to\zeta$ is expressed in terms of the lower density (with respect to plane Lebesgue measure) of the set $\mathbb C\setminus D$ at the point $\zeta$. 
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D. S. Telyakovskii. On the Phragmen--Lindelof principle for subharmonic functions. Izvestiya. Mathematics , Tome 63 (1999) no. 2, pp. 401-422. http://geodesic.mathdoc.fr/item/IM2_1999_63_2_a5/

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