Global solutions to special Lagrangian equations
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- by Yu Yuan PDF
- Proc. Amer. Math. Soc. 134 (2006), 1355-1358 Request permission
Abstract:
We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.References
- Jiguang Bao, Jingyi Chen, Bo Guan, and Min Ji, Liouville property and regularity of a Hessian quotient equation, Amer. J. Math. 125 (2003), no. 2, 301–316. MR 1963687, DOI 10.1353/ajm.2003.0007
- A. A. Borisenko, On a Liouville-type theorem for the equation of special Lagrangian submanifolds, Mat. Zametki 52 (1992), no. 5, 22–25, 140 (Russian, with Russian summary); English transl., Math. Notes 52 (1992), no. 5-6, 1094–1096 (1993). MR 1201944, DOI 10.1007/BF01236614
- L. Caffarelli, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985), no. 3-4, 261–301. MR 806416, DOI 10.1007/BF02392544
- Lawrence C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), no. 3, 333–363. MR 649348, DOI 10.1002/cpa.3160350303
- Lei Fu, An analogue of Bernstein’s theorem, Houston J. Math. 24 (1998), no. 3, 415–419. MR 1686614
- Reese Harvey and H. Blaine Lawson Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. MR 666108, DOI 10.1007/BF02392726
- N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487–523, 670 (Russian). MR 661144
- Johannes C. C. Nitsche, Elementary proof of Bernstein’s theorem on minimal surfaces, Ann. of Math. (2) 66 (1957), 543–544. MR 90833, DOI 10.2307/1969907
- Mao-Pei Tsui and Mu-Tao Wang, A Bernstein type result for special Lagrangian submanifolds, Math. Res. Lett. 9 (2002), no. 4, 529–535. MR 1928873, DOI 10.4310/MRL.2002.v9.n4.a13
- Yu Yuan, A Bernstein problem for special Lagrangian equations, Invent. Math. 150 (2002), no. 1, 117–125. MR 1930884, DOI 10.1007/s00222-002-0232-0
Additional Information
- Yu Yuan
- Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
- Email: yuan@math.washington.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1355-1358
- MSC (2000): Primary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-05-08081-0
- MathSciNet review: 2199179