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多复变与复几何系列报告

报告题目一： Smooth equivalence of deformations of domains in complex euclidean spaces

报告人：Prof. Xianghong Gong

(University of Wisconsin-Madison)

时间地点：2018年7月18日下午4:00-5:00，后主楼 1223

邀请人：汪志威

摘要：

We prove that two smooth families of 2-connected domains in the complex plane are smoothly equivalent if they are equivalent under a possibly discontinuous family of biholomorphisms. We construct, for m \geq 3,  two  smooth families of smoothly bounded m-connected domains in the complex plane, and for n\geq2, two families of strictly pseudoconvex domains in C^n, that are  equivalent under discontinuous families of biholomorphisms but not under any continuous family of biholomorphisms.  Finally, we give sufficient conditions for  the smooth equivalence of two smooth families of domains. This is joint work with Herv\'e Gaussier.

报告题目二： H?lder estimates for homotopy operators on strictly pseudoconvex domains with  C^2  boundary

报告人：Prof. Xianghong Gong

(University of Wisconsin-Madison)

时间地点：2018年7月20日下午4:00-5:00，后主楼 1223

邀请人：汪志威

摘要：

We derive a new homotopy formula for a strictly pseudoconvex domain of C^2  boundary in C^n by using a method of Lieb and Range and obtain estimates in H\"older-Zygmund spaces for the homotopy operators. In particular, this yields a sharp regularity for d-bar solutions.  We apply the estimates to obtain boundary regularities of D-solutions for a domain in C^n\times R^m.