A local obstruction for elliptic operators on flat germs

11.03.2021 09:00 - 10:30

Martino Fassina (University of Vienna)

In 1957 a ground-breaking three-page paper in the Annals marked the birth of CR geometry. There, Hans Lewy gave the first example of a locally non-solvable first-order linear partial differential equation. In this talk I will present a Lewy-type phenomenon for flat functions, that is, smooth functions whose derivatives are all equal to zero at a point. While such ''local flat non-solvability'' occurs for every elliptic operator with real analytic coefficients, I will focus mostly on the consequences on complex analysis. The talk is based on joint work with Yifei Pan.

Bernhard Lamel