Titles and Short Summaries of the Talks

37 Complex Analysis
14:20–15:20 Talk invited by Complex Analysis Section
Hidetaka Hamada
(Kyushu Sangyo Univ.)
♯ Loewner chains on complete hyperbolic complex manifolds
Final: 2013/2/7
Summary: We present a new geometric construction of Loewner chains in one and several complex
variables which holds on complete hyperbolic complex manifolds and show that there is essentially
a one-to-one correspondence between evolution families of order d and Loewner chains of the same
order. As a consequence, we obtain a univalent solution (ft : M → N) for any Loewner–Kufarev
PDE. We also show that a modified Roper–Suffridge extension operator preserves Loewner chains
of order d.