Euclidean Domains with Nearly Maximal Yamabe Quotient
Euclidean Domains with Nearly Maximal Yamabe Quotient
Let $\Omega$ be a smooth, bounded domain in $\mathbb R^3$ with connected boundary. It follows from work of Escobar that the Yamabe quotient of $\Omega$ is at most the Yamabe quotient of a ball, and equality holds if and only if $\Omega$ is a ball. We show that if equality …