ar X iv : m at h / 98 10 17 2 v 1 [ m at h . D G ] 2 9 O ct 1 99 8 VOLUME OF RIEMANNIAN MANIFOLDS , GEOMETRIC INEQUALITIES , AND HOMOTOPY THEORY

m at h . D G / 9 81 01 72 v 2 1 9 N ov 1 99 8 VOLUME OF RIEMANNIAN MANIFOLDS , GEOMETRIC INEQUALITIES , AND HOMOTOPY THEORY

We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X. In other words, orientable 4-man...

m at h . D G ] 1 9 N ov 1 99 8 VOLUME OF RIEMANNIAN MANIFOLDS , GEOMETRIC INEQUALITIES , AND HOMOTOPY THEORY

We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X. In other words, orientable 4-man...

Volume of Riemannian manifolds , geometric inequalities , and homotopy theory

We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X. In other words, orientable 4-man...

m at h . D G ] 1 2 Fe b 20 07 E 7 , WIRTINGER INEQUALITIES , CAYLEY 4 - FORM , AND HOMOTOPY

Pii: S0898-1221(97)00049-7

-In this paper, we establish the equivalence between the generalized nonlinear variational inequalities and the generalized Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities. We also discuss the convergence analysis of the proposed algorithms. As a special case, we obtain various known results...