A simple proof of curvature estimates for the 𝑛-1 Hessian equation

Ren and Wang [Amer. J. Math. 141 (2019), 1281–1315] proved the curvature estimates for the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n minus 1"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo> − </mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> curvature equation. The purpose of this note is to give a simple proof of their theorem.