Title: On the regularity of d-bar solutions on domains in complex manifolds satisfying condition a_q
Speaker: Xianghong Gong (University of Wisconsin-Mafison)
Speaker's URL: https://www.math.wisc.edu/~gong/
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 or 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.
URL associated with Seminar: https://u.osu.edu/hascv/