A Concavity Inequality for Hessian Quotient Equations
Yi-Lin Tsai
Abstract
We prove a concavity inequality for the Hessian quotient operator σk/σk-1 using a change of basis for symmetric polynomials. This removes an additional structural concavity assumption previously imposed in the interior C2 estimate for convex solutions of the σk/σk-1 equation. The method also yields several useful inequalities for elementary symmetric polynomials.
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