= Loewner correspondence theorem
{c}
{title2=$\partial_tg_t(z)=2/(g_t(z)-\xi_t)$}
An increasing family of <compact H-hulls> of <half-plane capacity> $2t$ with the <Loewner local growth property> corresponds uniquely to a continuous real <Loewner driving function>. Its <mapping-out functions> solve the <Chordal Loewner equation> up to the maximal lifetime of each point. Conversely each continuous driver generates that hull family. A continuous <Loewner trace> is an additional property, not a consequence for every continuous driver. For <SLE> it is supplied by the trace-existence theorem.
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