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Global solutions to special Lagrangian equations


Author: Yu Yuan
Journal: Proc. Amer. Math. Soc. 134 (2006), 1355-1358
MSC (2000): Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-05-08081-0
Published electronically: October 6, 2005
MathSciNet review: 2199179
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.


References [Enhancements On Off] (What's this?)

  • [BCGJ] Bao, J.-G., Chen, J.-Y., Guan, B., and Ji, M., Liouville property and regularity of a Hessian quotient equation, Amer. J. Math. 125 (2003), 301-316. MR 1963687 (2004b:35079)
  • [B] Borisenko, A. A., On a Liouville-type theorem for the equation of special Lagrangian submanifolds, (Russian) Mat. Zametki 52 (1992), 22-25; English translation in Math. Notes 52 (1992), 1094-1096 (1993).MR 1201944 (93k:53055)
  • [CNS] Caffarelli, L. A., Nirenberg, L., and Spruck, J., The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985), 261-301. MR 0806416 (87f:35098)
  • [E] Evans, L. C., Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), no. 3, 333-363. MR 0649348 (83g:35038)
  • [F] Fu, L., An analogue of Bernstein's theorem, Houston J. Math. 24 (1998), 415-419. MR 1686614 (2000c:53006)
  • [HL] Harvey, R. and Lawson, H. B., Jr., Calibrated geometry, Acta Math. 148 (1982), 47-157. MR 0666108 (85i:53058)
  • [K] Krylov, N. V., Boundedly nonhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 487-523 in Russian; English translation in Math. USSR Izv. 20(1983), 459-492.MR 0661144 (84a:35091)
  • [N] Nitsche, J. C. C., Elementary proof of Bernstein's theorem on minimal surfaces, Ann. of Math. 66 (1957), 543-544. MR 0090833 (19:878f)
  • [TW] Tsui, M.-P. and Wang, M.-T., A Bernstein type result for special Lagrangian submanifolds, Math. Res. Lett. 9 (2002), 529-535. MR 1928873 (2003k:53059)
  • [Y] Yuan, Y., A Bernstein problem for special Lagrangian equations, Invent. Math. 150 (2002), 117-125. MR 1930884 (2003k:53060)

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Additional Information

Yu Yuan
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email: yuan@math.washington.edu

DOI: https://doi.org/10.1090/S0002-9939-05-08081-0
Received by editor(s): September 9, 2004
Received by editor(s) in revised form: November 29, 2004
Published electronically: October 6, 2005
Additional Notes: The author was partially supported by an NSF grant and a Sloan Research Fellowship. The author was a visiting fellow at the Australian National University while this work was done.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2005 American Mathematical Society

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