Volume, diameter and the minimal mass of a stationary 1-cycle

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In this paper we present upper bounds on the minimal mass of a non-trivial stationary 1-cycle. The results that we obtain are valid for all closed Riemannian manifolds. The first result is that the minimal mass of a stationary 1-cycle on a closed n-dimensional Riemannian manifold M^n is bounded from above by (n+2)!d/3, where d is the diameter of a manifold M^n. The second result is that the minimal mass of a stationary 1-cycle on a closed Riemannian manifold M^n is bounded from above by 2(n+2)!Fill Rad(M^n) and, as a corollary, by 2(n+2)!(n+1)n^n(n!)^{1/2}(vol(M^n))^{1/n}, where Fill Rad(M^n) is the filling radius of the manifold, and vol(M^n) is its volume.
35 pages; 1 Figure

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Differential Geometry, Metric Geometry, Primary: 53C22, 53C23; Secondary: 49Q20

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http://salesiana.dossiersoluciones.com/handle/123456789/63218

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201269
 http://arxiv.org/abs/math/0201269

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arXiv