68 citations · 109 across the 23 of their papers we have counts for
23 papers
Hessian estimates for the sigma-2 equation in dimension four
Ravi Shankar, Yu Yuan
We derive a priori interior Hessian estimates and interior regularity for the equation in dimension four. Our method provides respectively a new proof for the corresponding t…
Rigidity for general semiconvex entire solutions to the sigma-2 equation
Ravi Shankar, Yu Yuan
We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions.
Regularity for convex viscosity solutions of special Lagrangian equation
Jingyi Chen, Ravi Shankar, Yu Yuan
We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of t…
Hessian estimate for semiconvex solutions to the sigma-2 equation
Ravi Shankar, Yu Yuan
We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre-Lewy transfor…
Maximal hypersurfaces over exterior domains
Guanghao Hong, Yu Yuan
In this paper, we study the exterior problem for the maximal surface equation. We obtain the precise asymptotic behavior of the exterior solution at infinity. And we prove that the…
Hessian estimates for convex solutions to quadratic Hessian equation
Matt McGonagle, Chong Song, Yu Yuan
We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.