A volume comparison theorem for Finsler manifolds
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- by Carlos E. Durán PDF
- Proc. Amer. Math. Soc. 126 (1998), 3079-3082 Request permission
Abstract:
Let $(M^{n},F)$ be a symmetric Finsler manifold, endowed with the Busemann volume form, and let $D$ be its unit disk bundle endowed with the canonical symplectic volume form. It is shown that $Vol(D)\leq C(n)Vol(M^{n})$, where $C(n)$ is the volume of the unit disk in ${\mathbb {R}}^{n}$. Moreover, equality holds if and only if $(M^{n},F)$ is Riemannian.References
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Additional Information
- Carlos E. Durán
- Affiliation: IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janerio RJ 22460-320, Brasil
- Address at time of publication: IVIC-Matematicas, Apartado 21827, Caracas 1020-A, Venezuela
- Email: cduran@impa.br, cduran@cauchy.ivic.ve
- Received by editor(s): March 6, 1997
- Additional Notes: Supported by CNPq, Brasil
- Communicated by: Christopher B. Croke
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3079-3082
- MSC (1991): Primary 53C60, 53C15
- DOI: https://doi.org/10.1090/S0002-9939-98-04629-2
- MathSciNet review: 1473664