K-cowaist on complete foliated manifolds

Let .M; F / be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric g TM .We generalize Gromov's K-cowaist using the coverings of M , as well as defining a closely related concept called the y A-cowaist.Let k F be the associated leafwise scalar curvature of g F D g TM j F .We obtain some estimates on k F using these two concepts.In particular, assuming that the generalized K-cowaist is infinity and either TM or F is spin, we show that inf.kF / 0. 58J20; 53C12, 53C21 2 In the literature, there are different ways to define the norm of R E (or R E z F); see eg [3; 12].Here, we adopt the same definition as in [14].However, for the content discussed in this paper, all these norms work.