an:04088443
Zbl 0665.53041
Gallot, Sylvestre
Isoperimetric inequalities based on integral norms of Ricci curvature
EN
Les processus stochastiques, Coll. Paul L??vy, Palaiseau/Fr. 1987, Ast??risque 157-158, 191-216 (1988).
1988
a
53C20 58J50
isoperimetric inequality; diameter; Ricci curvature; eigenvalues of the Laplacian; heat kernel; first Betti number; Gromov-norm
An isoperimetric inequality for domains in general Riemannian manifolds is obtained. A priori constants depend only on diameter and certain integral norms of the negative part of the Ricci curvature. This leads to estimates for eigenvalues of the Laplacian, for the heat kernel, and for the first Betti number of the manifold. Other interesting bounds are obtained for the Gromov-norm of homology classes of M.
For the entire collection see [Zbl 0649.00017].
K.Grove