Complex Analysis, Complex Geometry, Complex Differential Geometry (MSC 32).
The main interest of my research lies in
the interplay of analysis and geometry on singular spaces.
On complex manifolds, analytic methods have led to
fundamental advances in geometry (transcendental methods),
but most analytic tools are not very well developed on singular spaces.
It is a promising endeavor to create appropriate analytic instruments
in the presence of singularities.
On the other hand, this is not possible without considerable
insight in the geometric nature of the underlying space.
Particularly, I am interested in the theory of the Cauchy-Riemann-Operator and the d-bar-Neumann-Operator on singular spaces. The intention is to develop d-bar-methods - one of the most powerful tools in complex analysis - for such spaces. The focus lies on Lē-methods (which are most promising), but also integral formulas and other tools from Complex Geometry and Differential Geometry play a profound role. My research is concerned with the following topics: