Hall 123

Holomorphic extension of CR functions

R. Sivaguru

TIFR CAM

A submanifold $M$ of $\mathbb{C}^n$ is called CR if it admits a ``partial complex structure''. Functions on $M$ that are regular with respect to this structure are called CR functions. CR functions on $M$ are analogous to holomorphic functions in $\mathbb{C}^n$. In fact, the restriction of holomorphic functions to $M$ gives CR functions. So, a natural question that arises is -- when do CR functions on $M$ extend to holomorphic functions? We will review the known results and describe our contribution to this question. Our discussion will begin with the definitions of CR manifolds and CR functions and will include many examples. This is joint work with Ji\v{r}\'{\i} Lebl and Alan Noell.