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math.AP2020★ 1 cited
Weak Harnack inequalities for eigenvalues and constant rank theorems
Gábor Székelyhidi, Ben Weinkove
We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian-Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessi…
math.AP2015★ 1 cited
On a constant rank theorem for nonlinear elliptic PDEs
Gábor Székelyhidi, Ben Weinkove
We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of q…
math.AP2011
Periodic solutions of Abreu's equation
Renjie Feng, Gábor Székelyhidi
We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian var…