Generalized degree and optimal Loewner-type inequalities
微分几何
2007-05-23 v1 代数拓扑
几何拓扑
度量几何
摘要
We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool is the construction of an area-decreasing map to the Jacobi torus, streamlining and generalizing the construction of the first author in collaboration with D. Burago. It turns out that one can successfully combine this construction with the coarea formula, to yield new optimal inequalities.
引用
@article{arxiv.math/0405019,
title = {Generalized degree and optimal Loewner-type inequalities},
author = {Sergei V. Ivanov and Mikhail G. Katz},
journal= {arXiv preprint arXiv:math/0405019},
year = {2007}
}
备注
13 pages