University of Wisconsin
Open Search Candidate
, is it possible
to find a larger open set U containing V such that every holomorphic
function on V extends to a holomorphic function on U? If 
,
this is never possible. But in several variables this can sometimes be done,
and characterizing those sets for which extension is possible is a difficult
problem. Perhaps even more surprising is the fact that, under suitable hypotheses
on a hypersurface in ,
there may exist a common open set in
to which every sufficiently smooth solution to a certain system of partial
differential equations extends holomorphically. Furthermore, such an extension
phenomenon may even be observed for sets of higher codimension if they retain
some of the complex structure of the ambient space. These sets are the CR
manifolds. The associated partial differential equations are referred to
as the Cauchy-Riemann equations, and their solutions are the CR functions.
The problem of CR extension, then, is to understand under what conditions
there exists a common open set in
to which every CR function on a CR manifold extends holomorphically, and,
when CR extension is possible, to describe this set.
In this talk, I will discuss the properties we expect of the regions for CR extension. I will describe work on a model class of manifolds that illustrates the limitations of earlier descriptions of CR extension and develops an alternative meeting the proposed criteria.
4:10 p.m. in Skaggs117
Mathematical Sciences | The University of Montana
