Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2007, Volume 3, Number 3, Pages 298–312 (Mi jmag67)  
This article is cited in 1 scientific paper (total in 1 paper)

Some comparison theorems in Finsler–Hadamard manifolds

A. A. Borisenko, E. A. Olin

Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine
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Abstract: We give upper and lower bounds for the ratio of the volume of metric ball to the area of metric sphere in Finsler–Hadamard manifolds with the pinched S-curvature. We apply these estimates to find the limit at infinity for this ratio. The estimates derived are the generalization of the result well known in Riemannian geometry. We also estimate the volume growth entropy for the balls in these manifolds.
Key words and phrases: Finsler geometry, Finsler–Hadamard manifolds, comparison theorems, balls, volume and area, entropy.
Received: 24.10.2006
Bibliographic databases:
Document Type: Article
MSC: 53C60, 53C20
Language: English
Citation: A. A. Borisenko, E. A. Olin, “Some comparison theorems in Finsler–Hadamard manifolds”, Zh. Mat. Fiz. Anal. Geom., 3:3 (2007), 298–312
Citation in format AMSBIB
\Bibitem{BorOli07}
\by A.~A.~Borisenko, E.~A.~Olin
\paper Some comparison theorems in Finsler--Hadamard manifolds
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2007
\vol 3
\issue 3
\pages 298--312
\mathnet{http://mi.mathnet.ru/jmag67}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2330692}
\zmath{https://zbmath.org/?q=an:1144.53327}
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