The Monge-Ampère equation and warped products of higher rank
SourceJournal of the Australian Mathematical Society
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We show that a warped product Mf = ℝ × f ℝ has higher rank and nonpositive curvature if and only if f is a convex solution of the Monge-Ampère equation. In this case we show that M contains a Euclidean factor. © 2007 Australian Mathematical Society.