Gabriela Kohr
Gabriela Kohr
Gabriela Kohr
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5. Open problems<br />
Conjecture<br />
5. Open problems<br />
Let A ∈ L(X) be such that k+(A) < 2m(A). Also, let f (z, t) be an<br />
A-normalized univalent subordination chain f (z, t) such that the<br />
condition (4.4) holds. Then f = f (·, 0) has A-parametric representation.<br />
• In the case X = C n , every Loewner chain satisfies the generalized<br />
Loewner differential equation (Graham, Hamada, K, 2002).<br />
Problem<br />
Let A ∈ L(X) be such that k+(A) < 2m(A) and let f (z, t) be an<br />
A-normalized univalent subordination chain. Does there exist a<br />
generating vector field h(z, t) = Az + · · · such that<br />
∂f<br />
(z, t) = Df (z, t)h(z, t), a.e. t ≥ 0, ∀z ∈ B?<br />
∂t<br />
<strong>Gabriela</strong> <strong>Kohr</strong> (UBB Cluj) Geometric and analytic aspects of Loewner chains 57 / 62
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