A Bernstein Problem for Special Lagrangian Equations
نویسنده
چکیده
where λis are the eigenvalues of the Hessian D 2u. Namely, any global convex solution to (1.1) in R must be a quadratic polynomial. Recall the classical result, any global convex solution in R to the Laplace equation △u = λ1+ · · ·+λn = c or the Monge-Ampère equation log detD2u = log λ1+ · · ·+ log λn = c must be quadratic. Equation (1.1) originates from special Lagrangian geometry [HL]. The (Lagrangian) graph (x,▽u (x)) ⊂ R × R is called special when the argument of the complex number (
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