Title:
Hypersurfaces and isoperimetric inequalities in Cartan-Hadamard manifolds
Abstract: We prove a sharp generalization of Banchoff and
Pohl's isoperimetric inequality in complete, simply connected
Riemannian manifolds of non-positive sectional curvature. We also
prove a sharp, quantitative version of an isoperimetric inequality of
Yau in spaces of negative curvature and a modified version of Croke's
sharp 4-dimensional isoperimetric inequality. We discuss the
relationship between these results and the Cartan-Hadamard conjecture,
which states that complete, simply connected Riemannian manifolds with
non-positive curvature satisfy the Euclidean isoperimetric inequality.