Smooth compactness of $f$-minimal hypersurfaces with bounded $f$-index

Ezequiel Barbosa, Ben Sharp, Yong Wei

Let $(M^{n+1},g,e^{-f}d\mu )$ be a complete smooth metric measure space with $2\le n\le 6$ and Bakry-Émery Ricci curvature bounded below by a positive constant. We prove a smooth co…