A maximum rank problem for degenerate elliptic fully nonlinear equations

Abstract

The solutions to the Dirichlet problem for two degenerate elliptic fully nonlinear equations in $n+1$ dimensions, namely the real Monge-Ampère equation and the Donaldson equation, are shown to have maximum rank in the space variables when $n\le 2$. A constant rank property is also established for the Donaldson equation when $n=3$.

References in corpus (2)

• The Donaldson equation
• The space of volume forms