# Dror Varolin: L^2 extension of dbar-closed forms from a smooth complex hypersurface

Source: Complex analysis seminar

V torek, 15. maja ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predaval prof. Dror Varolin z univerze SUNY-Stony Brook, New York, ZDA.

Title: L^2 extension of dbar-closed forms from a smooth complex hypersurface.

Abstract: The L^2 extension of holomorphic functions and holomorphic sections of holomorphic line bundles has been proved in numerous contexts by a number of people, starting with Ohsawa and Takegoshi. The corresponding result for dbar-closed forms of bidegree (0,q) for q>0 has been open for a long time. For one thing, there are two natural possible meanings for extension of (0,q)-forms from a hypersurface: the first (which we call 'intrinsic' is that the pullback of the extension by the natural inclusion is specified, while the second (which we call 'ambient') is that the restriction of the (0,q)-form in the ambient space is specified; in the ambient case one has to say what it means to be the restriction of a dbar-closed form.

The extension result (without specification of the type of extension) was claimed by Manivel, but his proof contained a gap which was pointed out by Demailly. Koziarz proved that it is possible to carry out intrinsic extension (0,q) cohomology classes, but the estimates he obtained are not sufficient for many applications. Very recently, Berndtsson established the intrinsic extension theorem for q>0 and with good estimates, under the assumption that the underlying manifold is compact.

In this talk, I will describe joint work with Jeff McNeal in which we establish both kinds of extension theorems for dbar-closed (0,q)-forms from a smooth complex hypersurface in a Stein manifold.

Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!

Vodji seminarja

Josip Globevnik in Franc Forstneric