Jakob Loren

Sharp Yamabe Bounds for Spherical Three-Space Forms via Four-Dimensional Poincar\'e--Einstein Compactness

Let $\Gamma<SO(4)$ be a nontrivial finite group acting freely on $S^3$, and let $M=S^3/\Gamma$. We prove that every smooth conformal class $C$ on $M$ satisfies \[ Y(M,C)\le |\Gamma|^{-2/3}Y(S^3), \] with equality for the quotient-round conformal class. Consequently, \[ \sigma(M)=|\Gamma|^{-2/3}Y(S^3). \] Our approach u...