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题目：½ estimate for global Newlander-Nirenberg theorem on strongly pseudoconvex domains

报告人：师子鸣教授 (Rutgers University-New Brunswick)

Abstract:

Given a formally integrable almost complex structure X defined on the closure of a bounded domain , and provided that X is sufficiently close to the standard complex structure, the global Newlander-Nirenberg problem asks whether there exists a global diffeomorphism defined on  that transforms X into the standard complex structure, under certain geometric and regularity assumptions on D. In this paper we prove a quantitative result of this problem. Assuming D is a strongly pseudoconvex domain in  with  boundary, and that the almost complex structure X is of the H\"older-Zygmund class  for , we prove the existence of a global diffeomorphism (independent of ) in the class $$, for any . The main ideas of the proof are construction of Moser-type smoothing operator bounded Lipschitz domains and an iteration scheme of KAM type.

报告时间：2023-7-17周一上午9:20-10:20

报告地点：校本部教二楼 613教室

邀请人：戎小春、胥世成