Eigenvalue comparison theorems on Finsler manifolds

2014 ◽  
Vol 36 (1) ◽  
pp. 31-44 ◽  
Author(s):  
Songting Yin ◽  
Qun He
Keyword(s):  
Comparison Theorems ◽  
Finsler Manifolds ◽  
Eigenvalue Comparison

Some eigenvalue comparison theorems of Finsler p-Laplacian

2018 ◽  
Vol 29 (06) ◽  
pp. 1850044
Author(s):  
Songting Yin ◽  
Qun He
Keyword(s):  
Riemannian Geometry ◽  
Type Inequality ◽  
Finsler Manifold ◽  
Comparison Theorems ◽  
Flag Curvature ◽  
First Eigenvalue ◽  
Constant Flag Curvature ◽  
The First Eigenvalue ◽  
Negative Constant ◽  
Eigenvalue Comparison

We obtain Cheng type inequality, Cheeger type inequality, Faber–Krahn type inequality and McKean type inequality of [Formula: see text]-Laplacian on a Finsler manifold. These generalize the corresponding theorems in Riemannian geometry and sharpen some results in recent literatures. Moreover, for a complete noncompact Finsler manifold with negative constant flag curvature and vanishing [Formula: see text] curvature, the first eigenvalue is calculated.

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