arXiv Analytics

Sign in

arXiv:math/9810172 [math.DG]AbstractReferencesReviewsResources

Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

Mikhail G. Katz, Alexander I. Suciu

Published 1998-10-29, updated 1998-11-19Version 2

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.

Comments: 25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math
Journal: Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 113-136, Contemp. Math., vol. 231, Amer. Math. Soc., Providence, RI, 1999
Categories: math.DG, math.AT
Subjects: 53C23, 55Q15
Related articles: Most relevant | Search more
arXiv:1009.2637 [math.DG] (Published 2010-09-14, updated 2011-06-19)
Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
arXiv:1010.4514 [math.DG] (Published 2010-10-21, updated 2014-01-24)
Existence of Integral $m$-Varifolds minimizing $\int |A|^p$ and $\int |H|^p$, $p>m$, in Riemannian Manifolds
arXiv:0801.2216 [math.DG] (Published 2008-01-15, updated 2008-08-25)
Knots in Riemannian manifolds

Links

Toolbox