Journal
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume 62, Issue 2, Pages 320-354Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.4153/CJM-2010-019-8
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Funding
- National Science and Engineering Research Council of Canada [261955]
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The space of Monge Ampere functions, introduced by J. H. G. Fu, is a space of rather rough functions in which the map u (sic) Det D(2)u is well defined and weakly continuous with respect to a natural notion of weak convergence. We prove a rigidity theorem for Lagrangian integral currents that allows us to extend the original definition of Monge-Ampere functions. We also prove that if a Monge-Ampere function u on a bounded set Omega subset of R-2 satisfies the equation Det D(2)u = 0 in a particular weak sense, then the graph of u is a developable surface, and moreover u enjoys somewhat better regularity properties than an arbitrary Monge Ampere function of 2 variables.
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