Some Rigidity Results Related to Monge-ampère Functions
نویسندگان
چکیده
The space of Monge-Ampère functions, introduced by J. H. G. Fu in [7, 8] is a space of rather rough functions in which the map u 7→ Det D 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-Ampère functions given in [7]. We also prove that if a Monge-Ampère function u on a bounded set Ω ⊂ R satisfies the equation Det Du = 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 MongeAmpère function of 2 variables.
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