2002
DOI: 10.1007/s00222-002-0232-0
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A Bernstein problem for special Lagrangian equations

Abstract: We derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyper-plane.Comment: 9 pages, submitted on December 10, 200

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Cited by 116 publications
(125 citation statements)
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“…A useful formula for the minimal Lagrangian graph is derived by applying Wang's Bochner formula to the quaternionic frame. Using this formula, we obtain some Bernstein theorems for Σ, which generalize those results in [8] and [11] (see Section 3 for details). Obviously, when u 2 and u 3 are constant, Σ is just the special Lagrangian graph in C n .…”
Section: §1 Introductionmentioning
confidence: 81%
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“…A useful formula for the minimal Lagrangian graph is derived by applying Wang's Bochner formula to the quaternionic frame. Using this formula, we obtain some Bernstein theorems for Σ, which generalize those results in [8] and [11] (see Section 3 for details). Obviously, when u 2 and u 3 are constant, Σ is just the special Lagrangian graph in C n .…”
Section: §1 Introductionmentioning
confidence: 81%
“…Tsui and Wang in [8] obtained Bernstein results for special Lagrangian graphs by applying the same Bochner formula. We should point out that the same formula for special Lagrangian graphs was also derived by Yuan in [11] from a different point of view. An important technique used by Yuan is the so-called Lewy transformation which allows him to prove: Any special Lagrangian graph given by a convex potential function must be an affine plane.…”
Section: §1 Introductionmentioning
confidence: 98%
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“…The advantage of this kind of map is that we can find a good representation of via Lewy transformation. This technique is used by Yuan [2002] to prove a Bernstein theorem for special Lagrangian graphs. The difficult is that this case is noncompact.…”
Section: Introductionmentioning
confidence: 99%