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We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.
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참고문헌 (12)
참고문헌 신청
D. Bao / 2000 / An Introduction to Riemann-Finsler Geometry / Springer-Verlag
M. Gromov / 1981 / Structures metriques pour les varietes riemanniennes / CEDIC
Z. Shen / 1997 / Volume comparison and its applications in Riemann-Finsler geometry / Adv. Math 128(2):306~328
Z. Shen / 2001 / Lectures on Finsler Geometry / World Scientific Publishing Co
Y.-B. Shen / 2010 / Gromov pre-compactness theorems for nonreversible Finsler manifolds / Differential Geom. Appl 28(5):565~581
M. Gromov / 1981 / Structures metriques pour les varietes riemanniennes / CEDIC
Z. Shen / 1997 / Volume comparison and its applications in Riemann-Finsler geometry / Adv. Math 128(2):306~328
Z. Shen / 2001 / Lectures on Finsler Geometry / World Scientific Publishing Co
Y.-B. Shen / 2010 / Gromov pre-compactness theorems for nonreversible Finsler manifolds / Differential Geom. Appl 28(5):565~581
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