Xianghong Gong: On the regularity of d-bar solutions on domains in complex manifolds satisfying condition a_q

Datum objave: 20. 5. 2022
Seminar za kompleksno analizo
četrtek
26
maj
Ura:
12.15
Lokacija:
Predavalnica 3.07
ID: 940 4904 5946 – Geslo: 723320

V ČETRTEK, 26. maja ob 12. uri in 15 MINUT, bo v okviru seminarja za kompleksno analizo predaval prof. Xianghong Gong z University of Wisconsin-Madison, ZDA.

Title: On the regularity of d-bar solutions on domains in complex manifolds satisfying condition a_q.

Abstract: We will start with some recent regularity results for the d-bar equation on strictly pseudoconvex domains with C^2 boundary in the complex Euclidean space C^n. These results have been proved by using homotopy formulas and estimates hold for forms that are not necessarily d-bar closed. We will then describe new regularity results for the d-bar equation on a domain in a complex manifold when the boundary of the domain has either a sufficient number of positive Levi eigenvalues or a sufficient number of negative Levi eigenvalues. We will prove the same regularity result for given forms of type (0,1). For forms of type (0,q) with q>1, the same regularity for the d-bar solutions holds when the boundary is sufficiently smooth. Finally, we will mention an unsolved problem on the regularity of the homotopy formula when (0,1) forms are not d-bar closed, showing a subtle difference between negative and positive Levi eigenvalues.

Predavanje bo potekalo HIBRIDNO, v PREDAVALNICI 3.07 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/94049045946?pwd=T3VxZHMvY3JlaUFlVXYrSlg0Wm5zZz09

Meeting ID: 940 4904 5946 Passcode: 723320

Vljudno vabljeni!

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Franc Forstneric in Barbara Drinovec Drnovsek