@article{3341c6db5a624ba9b3c954c6fa084387,
title = "ON THE GLOBAL WELL-POSEDNESS OF THE ONE-DIMENSIONAL SCHR{\"O}DINGER MAP FLOW",
abstract = "We establish the global well-posedness of the initial value problem for the Schr{\"o}dinger map flow for maps from the real line into K{\"a}hler manifolds and for maps from the circle into Riemann surfaces. This partially resolves a conjecture of W.-Y. Ding.",
keywords = "Cubic nls, K{\"a}hler manifolds, Periodic nls, Schr{\"o}dinger flow, Strichartz estimates",
author = "Igor Rodnianski and Rubinstein, {Yanir A.} and Gigliola Staffilani",
note = "Funding Information: The authors are grateful to the referee for a careful reading and helpful suggestions that improved the article. They also thank B. Dai for a careful reading and for correcting an error in the computation of the holonomy in an earlier version of this article. This material is based upon work supported in part under National Science Foundation Graduate and Postdoctoral Research Fellowships and grants DMS-0406627, 0702270, 0602678. Rubinstein was also supported by graduate fellowships at MIT and at Princeton University, and by a Clay Mathematics Institute Liftoff Fellowship. This work was mostly carried out while Rodnianski was visiting MIT in Spring 2006, and while Rubinstein was visiting Princeton University in Spring 2008, and the authors thank these institutions for their hospitality. Publisher Copyright: {\textcopyright} 2009,Analysis and PDE.All Rights Reserved",
year = "2009",
doi = "10.2140/apde.2009.2.187",
language = "English (US)",
volume = "2",
pages = "187--209",
journal = "Analysis and PDE",
issn = "2157-5045",
publisher = "Mathematical Sciences Publishers",
number = "2",
}