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Disputation Hanxing Lin

09.12.2021 | 16:00
Thema der Dissertation:
Parqueting-Reflection Principle and Boundary Value Problems in Some Circular Polygons
Thema der Disputation:
Residual Cauchy-Type Formula on Riemann Surfaces
Abstract: Integral representation formulas contribute constructive methods for the function theory of several complex variables. Theory of functions on complex manifolds develops the subject from this constructive viewpoint. Some fundamental problems for complex manifolds, e.g. ∂¯-equation, Cousin problems, Levi problem, et al., can be solved by means of explicit integral representations.
In this talk, we first recall the Martinelli-Bochner formula, the Leray formula, and the Koppelman formula. Then we present a Cauchy-Weil-Leray type integral formula for differential forms on a domain in CPn by Henkin and Polyakov. We finally show the recent work from Polyakov about the con-struction of a Cauchy-type formula on open subdomains of Riemann surfaces which can be embedded into CP2.

Zeit & Ort

09.12.2021 | 16:00