Geometric Description of Some Loewner Chains with Infinitely Many Slits.

We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers (b n) n ≥ 1 and points of the real line (k n) n ≥ 1 , we explicitily solve the Loewner PDE ∂ f ∂ t (z , t) = - f ′ (z , t) ∑ n = 1 + ∞ 2 b n z - k n 1 - t <graphic href="12220_2024_1718_Article_Equ19.gif"></graphic> in H × [ 0 , 1) . Using techniques involving the harmonic measure, we analyze the geometric behaviour of its solutions, as t → 1 - . [ABSTRACT FROM AUTHOR]