Convex trigonometry with applications to sub-Finsler geometry
نویسندگان
چکیده
منابع مشابه
Harmonic Symmetrization of Convex Sets and of Finsler Structures, with Applications to Hilbert Geometry
David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm of a tangent vector from the distance f...
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We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملrelative volume comparison theorems in finsler geometry and their applications
we establish some relative volume comparison theorems for extremal volume forms of finsler manifolds under suitable curvature bounds. as their applications, we obtain some results on curvature and topology of finsler manifolds. our results remove the usual assumption on s-curvature that is needed in the literature.
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We prove Hessian comparison theorems, Laplacian comparison theorems and volume comparison theorems of Finsler manifolds under various curvature conditions. As applications, we derive Mckean type theorems for the first eigenvalue of Finsler manifolds, as well as generalize a result on fundamental group due to Milnor to Finsler manifolds.
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ژورنال
عنوان ژورنال: Sbornik: Mathematics
سال: 2019
ISSN: 1064-5616,1468-4802
DOI: 10.1070/sm9134