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Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

Mikhail G. Katz·Alexander I. Suciu
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Abstract

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.

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Mikhail G. Katz, Alexander I. Suciu. 1998-11-19. Volume of Riemannian manifolds, geometric inequalities, and homotopy theory. https://arxiv.org/abs/math/9810172

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