The Cauchy transform is a fundamental tool in the study of functions of one complex variable; unfortunately no direct analogue exists in higher dimensions. However, on hypersurfaces in ℂn satisfying a certain convexity condition, we may define the Leray transform which recaptures many key properties of the Cauchy transform. We study the Leray transform on certain families of unbounded hypersurfaces, some of which can be used to locally approximate any ℂ-convex hypersurface. These hypersurfaces generalize the Heisenburg group, and their group structure is essential to our analysis. We will go to examine these results in the context of projective dual CR structure and present a universal formulation of the Leray transform.
The Leray transform: Model hypersurfaces and dual CR structures in ℂℙ²
18.03.2021 09:00 - 10:30
Organiser:
Bernhard Lamel
Location:
Zoom