THE WILLMORE FUNCTIONAL ON LAGRANGIAN TORI - ITS RELATION TO AREA AND EXISTENCE OF SMOOTH MINIMIZERS
成果类型：
Article
署名作者：
MINICOZZI, WP
刊物名称：
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN/ISSBN：
0894-0347
DOI：
10.1090/S0894-0347-1995-1311825-9
发表日期：
1995
页码：
761-791
关键词：
摘要：
In this paper we prove an existence and regularity theorem for lagrangian tori minimizing the Willmore functional in Euclidean four-space, R(4), with the standard metric and symplectic structure. Technical difficulties arise because the Euler-Lagrange equation for this problem is a sixth-order nonlinear partial differential equation. This research was motivated by a study of the seemingly unrelated Plateau problem for lagrangian tori, and in this paper we illustrate this connection.
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