Eigenvalue comparison theorems on Finsler manifolds

Yin, Songting; He, Qun

doi:10.1007/s11401-014-0879-z

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…Nonetheless, we investigated the nonlinear heat flow associated with the nonlinear Laplacian in [OS1], and established the Bochner inequality in [OS3]. This Bochner inequality has many applications including gradient estimates ( [OS3,Oh7]) and various eigenvalue estimates ( [WX,YH1,YH2,Xi]).…”

Section: Introductionmentioning

confidence: 99%

Some functional inequalities on non-reversible Finsler manifolds

Ohta

2017

Proc Math Sci

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We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the Γ-calculusà la Bakry et al, we show the dimensional versions of the Poincaré-Lichnerowicz inequality, the logarithmic Sobolev inequality, and the Sobolev inequality. In the reversible case, these inequalities were obtained by Cavalletti-Mondino in the framework of curvature-dimension condition by means of the localization method. We show that the same (sharp) estimates hold also for non-reversible metrics.

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Section: Introductionmentioning

confidence: 99%

Some functional inequalities on non-reversible Finsler manifolds

Ohta

2017

Proc Math Sci

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“…After that, Wu-Xin ( [21]) proved Mckean type inequalities, while Chen ([2]) gained the Cheeger type inequality and also improved the Cheng type inequality obtained by Shen. There is still plenty of scope for improvement. Recently, some refinements of the results above were achieved by Yin-He in [24]. As for the first new lower bounds of the first eigenvalue on finsler manifolds Neumann and closed eigenvalues, ) gave a sharp lower bound estimation on Finsler manifolds with weighted Ricci curvature conditions (see Lemma 2.1 below).…”

Section: Introductionmentioning

confidence: 92%