Geometric inequalities involving three quantities in warped product manifolds

In this paper, we establish two families of sharp geometric inequalities for closed hypersurfaces in space forms or other warped product manifolds. Both compare three distinct quantities. The first family concerns the k-th boundary momentum, area and weighted volume, has applications to Weinstock-type Steklov Wentzell eigenvalues on star-shaped mean convex domains. This generalizes main results [12] confirms a conjecture posed therein. second involves curvature integral quermassintegrals. It authors' recent work [33] with G. Wheeler V.-M. Wheeler, author's [43] T. Zhou, different aspects.