Yamabe invariant

The Yamabe invariant is an important concept in differential geometry, particularly in the study of conformal classes of Riemannian metrics. It is named after the Japanese mathematician Hidehiko Yamabe, who contributed significantly to the field. Formally, the Yamabe invariant is defined for a compact Riemannian manifold \( M \) and is associated with the problem of finding a metric in a given conformal class that has constant scalar curvature.