Yu YUAN

• Quadratic Hessian equation.  

• Regularity for the Monge-Ampere equation by doubling,   Math. Z. to appear (with R. Shankar).

• Hessian estimates for the sigma-2 equation in dimension four,   submitted (with R. Shankar).

• A monotonicity approach to Pogorelov's Hessian estimates for Monge-Ampere equation,   Mathematics in Engineering, Math. Eng. 5 (2023), no. 2, Paper No. 037, 6 pp.

• Regularity for convex viscosity solutions of special Lagrangian Equation,    Comm. Pure Appl. Math. 76 (2023), no. 12, 4075--4086 (with J.Y. Chen and R. Shankar).

• Singular solutions to Monge-Ampere equation,    Anal. Theory Appl. 38 (2022), no. 2, 121--127 (with L. A. Caffarelli).

• Rigidity for general semiconvex entire solutions to the sigma-2 equation,    Duke Math. J. 171 (2022), no. 15, 3201--3214 (with R. Shankar).

• Regularity for almost convex viscosity solutions of the sigma-2 equation,    J. Math. Study 54 (2021), no. 2, 164--170 (with R. Shankar).

• Maximal hypersurfaces over exterior domains,    Comm. Pure Appl. Math. 74 (2021), 589--614 (with G.-H. Hong).

• Hessian estimate for semiconvex solutions to the sigma-2 equation,    Calc. Var. Partial Differential Equations 59 (2020), no. 1, Paper No. 30, 12 pp. (with R. Shankar).

• A Bernstein problem for special Lagrangian equations in exterior domains,    Adv. Math. 361 (2020), 106927, 29 pp. (with D.-S. Li and Z.-S. Li).

• Special Lagrangian equations,    Geometric Analysis, 521--536, Progress in Mathematics Series, 333, Birkhauser/Springer, Cham, 2020.

• Hessian estimates for convex solutions to quadratic Hessian equation,    Ann. Inst. H. Poincaré Anal. Non Linéaire, 36 (2019), no. 2, 451--454, (with M. McGonagle and C. Song).

• A pointwise approach to rigidity of almost graphical self-shrinking solutions of mean curvature flows,   Proc. Amer. Math. Soc. 146 (2018), 3057--3061, (with D.-S. Li and Y.-F. Xu).

• Hamiltonian stationary cones with isotropic links,   Pacific J. Math. 295 (2018), 317--327, (with J.-Y. Chen).

• Rigidity of complete entire self-shrinking solutions to Kahler-Ricci flow,   Int. Math. Res. Not. IMRN 2015, no. 12, 3908--3916 (with G. Drugan and P. Lu).

• Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions,   Amer. J. Math., 136 (2014), no.2, 481--499 (with D.-K. Wang).

• Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems,   Amer. J. Math., 135 (2013), 1157--1177 (with D.-K. Wang).

• Lagrangian mean curvature flow for entire Lipschitz graphs II,   Math. Ann., 357 (2013), 165--183 (with A. Chau and J.-Y. Chen).

• Rigidity of entire self-shrinking solutions to curvature flows,   J. Reine Angew. Math., 664 (2012), 229--239. (with A. Chau and J.-Y. Chen).

• A priori estimates for the Lagrangian mean curvature flows,   Int. Math. Res. Not., no. 19 (2011), 4376--4338 (with T. Nguyen).

• A Liouville problem for the Sigma-2 equations,    Discrete Contin. Dyn. Syst., 28 (2010), 659--664 (with S.-Y. A. Chang).

• Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase,   Amer. J. Math., 132 (2010), 751--770 (with M. Warren).

• Explicit gradient estimates for minimal Lagrangian surfaces of dimension two,   Math. Z., 262 (2009), 867--879 (with M. Warren).

• A priori estimate for convex solutions to special Lagrangian equations and its application,  Comm. Pure Appl. Math., 62 (2009), 583--595 (with J.-Y. Chen and M. Warren).

• Hessian estimates for the sigma-2 equation in dimension three,   Comm. Pure Appl. Math., 62 (2009), 305--321 (with M. Warren).

• A Liouville type theorem for special Lagrangian Equations with constraints,  Comm. Partial Differential Equations, 33 (2008), 922--932 (with M. Warren).

• Improving Pogorelov's isometric embedding counterexample,   Calc. Var. Partial Differential Equations, 32 (2008), 319--323 (with N. Nadirashvili).

• Minimal cones with isotropic links,   Int. Math. Res. Not. 2006, Art. ID 69284, 14 pp., (with J.Y. Chen).

• Resolving the singularity of minimal Hopf cones,   J. Partial Differential Equations, 19 (2006), no.3, 218--231 (with W.-Y. Ding).

• Global solutions to special Lagrangian equations,   Proc. Amer. Math. Soc., 134 (2006), 1355-1358.

• Homogeneous solutions to fully nonlinear elliptic equations,   Proc. Amer. Math. Soc., 134 (2006), 1647--1649 (with N. Nadirashvili).

• Linearity of homogeneous order one solutions to elliptic equations in dimension three,   Comm. Pure Appl. Math., 56 (2003), 425--432 (with Q. Han and N. Nadirashvili).

• A Bernstein problem for special Lagrangian equations,   Invent. Math., 150 (2002), 117--125.

• Locally minimizing smooth harmonic maps from asymptotically flat manifolds into spheres,   J. Partial Differential Equations, 15 (2002), no.4, 13--27.

• A priori estimates for solutions of fully nonlinear special Lagrangian equations,   Ann. Inst. H. Poincaré Anal. Non Linéaire, 18 (2001), 261--270.

• A priori estimates for solutions of fully nonlinear equations with convex level set,   Indiana Univ. Math. J., 49 (2000), 681--695 (with L. A. Caffarelli).

• Doubling properties for second order parabolic equations,   Ann. of Math., 150 (1999), 313--327 (with M. V. Safonov).

• Behavior near the boundary of positive solutions of second order parabolic equations II,   Trans. Amer. Math. Soc., 351 (1999), 4947--4961 (with E. B. Fabes and M. V. Safonov).