Abstract
AbstractThis paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a minimal foliation is called stable if for any small perturbation of the variational problem there exists a minimal foliation conjugate under a smooth diffeomorphism to the original foliation. In this paper the stability of special foliations of codimension 1 on a higher-dimensional torus is established. This result requires small divisor assumptions similar to those encountered in dynamical systems. This theorem can be viewed as a generalization of the perturbation theory of invariant tori for Hamiltonian systems to elliptic partial differential equations for which one obtains quasi-periodic solutions.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference24 articles.
1. A homological characterization of foliations consisting of minimal surfaces
2. KAM theory in configuration space;Salamon;Comm. Math. Helv.,1988
3. Über die Existenz kanonischer Transformationen bei mehreren unabhängigen Veränderlichen
4. [17] Moser, J. . Minimal foliations on a torus. Four lectures at CIME Conf. on Topics in Calculus of Variations (1987). To be published in Springer Lecture Notes in Mathematics.
5. A rapidly convergent iteration method and nonlinear differential equations, I and II;Moser;Ann. Scuola Norm. Sup.,1966
Cited by
47 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献