Obata theorem of ${\sigma }_k$-flat and constant associated $k$th boundary curvature equation

Abstract

On the upper hemisphere, we use the Obata-Escobar argument to establish an Obata theorem for ${\sigma }_k$-flat and positive constant boundary ${\mathcal{B}}_k$-curvature equation, which was initiated by Case-Wang [Adv. Math. 337 (2018), 83-106].

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