题目: Nonlinear Riemann-Hilbert problems for axial-monogenic functions
报告人：Prof. Uwe Kaehler, University of Aveiro, Portugal
摘要: One of the classic topics in Complex Analysis is the study of Riemann-Hilbert (RH) problems. Usually, theses problems are either transformed into a jump problem for the Cauchy-Riemann operator or in a problem of Wiener-Hopf factorization. In higher dimensions the problem becomes much more difficult due to the lack of a good logarithm function as well as the complicated structure of quaternionic linear algebra. After a short review of the state of the art on RH problems we are going to discuss the case of axial-monogenic functions. In this case the problem can be reduced to the study of a RH problem for a Vekua system, i.e. for generalized holomorphic functions. This will allow us to discuss the solution of nonlinear RH problems in the case of axial-monogenic functions.