Rigidity for the hyperbolic Monge-Ampere equation
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Submission date: 29. Jun. 2003 (revised version: May 2004)
published in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 3 (2004) 3, p. 609-623
DOI number (of the published article): 10.2422/2036-2145.2004.3.06
MSC-Numbers: 35L70, 49J10, 74G65
Keywords and phrases: rigidity, hyperbolic monge-ampere
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In this paper, we consider the model case when the compact set K is contained in the hyperboloid , which is a subset of symmetric matrices. The hyperboloid is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampere equation . 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.