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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
53/2003

Rigidity for the hyperbolic Monge-Ampere equation

Chun-Chi Lin

Abstract

In this paper, we consider the model case when the compact set $K$ is contained in the hyperboloid ${H}_{-1}$, which is a subset of symmetric $2\times 2$ matrices. The hyperboloid ${H}_{-1}$ is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampere equation $\det\nabla ^{2}u=-1$. For some compact subsets $K$ containing rank-one connection, we show the rigidity property of $K$ by imposing proper topology for the convergence of approximate solutions and affine boundary conditions.

Received:
Jun 29, 2003
Published:
Jun 29, 2003
MSC Codes:
35L70, 49J10, 74G65
Keywords:
rigidity, hyperbolic monge-ampere

Related publications

inJournal
2004 Repository Open Access
Chun-Chi Lin

Rigidity for the hyperbolic Monge-Ampere equation

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 3 (2004) 3, pp. 609-623