The Willmore Functional on Lagrangian Tori: Its Relation to Area and Existence of Smooth Minimizers
نویسنده
چکیده
In this paper we prove an existence and regularity theorem for la-grangian tori minimizing the Willmore functional in Euclidean four-space, R4 ,with the standard metric and symplectic structure. Technical difficulties arisebecause the Euler-Lagrange equation for this problem is a sixth-order nonlinearpartial differential equation. This research was motivated by a study of theseemingly unrelated Plateau problem for lagrangian tori, and in this paper weillustrate this connection. DEPARTMENT OF MATHEMATICS, STANFORD UNIVERSITY, STANFORD, CALIFORNIA 94305-2125 COURANT INSTITUTE OF MATHEMATICAL SCIENCES, 251 MERCER STREET, NEW YORK, NEWYORK 10012E-mail address: minicozzClcims.nyu.edu License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
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تاریخ انتشار 2009