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UID:24bed58a0a9089212130cfe5d61b31c7
CATEGORIES:Complex Analysis and Geometry Seminar
CREATED:20230404T132645
SUMMARY:½ estimate for global Newlander-Nirenberg theorem on strongly pseudoconvex domains
LOCATION:Hill Center Room 705
DESCRIPTION:<p><span style="color: #000000; font-family: Calibri, Arial, Helvetica, san
 s-serif; font-size: 16px; font-style: normal; font-weight: 400; letter-spac
 ing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transfor
 m: none; white-space: normal; widows: 2; word-spacing: 0px; background-colo
 r: #ffffff; float: none;">Abstract: Given a formally integrable almost comp
 lex structure \(X\) defined on the closure of a bounded domain \(D \subset 
 \mathbb C^n\), and provided that \(X\)is sufficiently close to the standard
  complex structure, the global Newlander-Nirenberg problem asks whether the
 re exists a global diffeomorphism defined on \(\overline D\) that transform
 s \(X\) into the standard complex structure, under certain geometric and re
 gularity assumptions on \(D\).&nbsp;</span><span style="border: 0px; font-s
 tyle: normal; font-weight: 400; font-size: 16px; line-height: inherit; font
 -family: Calibri, Arial, Helvetica, sans-serif; margin: 0px; padding: 0px; 
 vertical-align: baseline; color: #000000; letter-spacing: normal; orphans: 
 2; text-align: start; text-indent: 0px; text-transform: none; white-space: 
 normal; widows: 2; word-spacing: 0px;">In this talk, I will present my rece
 nt result on</span><span style="border: 0px; font-style: normal; font-weigh
 t: 400; font-size: 16px; line-height: inherit; font-family: Calibri, Arial,
  Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-align: baseline
 ; color: #000000; letter-spacing: normal; orphans: 2; text-align: start; te
 xt-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-
 spacing: 0px; background-color: #ffffff;">&nbsp;the&nbsp;<span style="borde
 r: 0px; font: inherit; margin: 0px; padding: 0px; vertical-align: baseline;
  color: inherit;">½</span>&nbsp;estimate for global Newlander-Nirenberg pro
 blem on strongly pseudoconvex domains. The main ingredients in our proof ar
 e the construction of Moser-type smoothing operators on bounded Lipschitz d
 omains using Littlewood-Paley theory and a convergence scheme of KAM type.&
 nbsp;</span></p>
CONTACT:Ziming Shi (Rutgers) 
DTSTAMP:20260907T130911
DTSTART;TZID=America/New_York:20230407T103000
DTEND;TZID=America/New_York:20230407T113000
SEQUENCE:0
TRANSP:OPAQUE
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