A Global Poincaré inequality on Graphs via a Conical Curvature-Dimension Condition

IF 0.9 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2018-02-16 DOI:10.1515/agms-2018-0002

Sajjad Lakzian, Zachary Mcguirk

引用次数: 6

Abstract

Abstract We introduce and study the conical curvature-dimension condition, CCD(K, N), for finite graphs.We show that CCD(K, N) provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs. Another application of the conical curvature-dimension analysis is finding a sharp estimate on the curvature of complete graphs

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基于圆锥曲率维数条件的图上的全局Poincaré不等式

摘要引入并研究了有限图的圆锥曲率维条件CCD(K, N)。我们证明了CCD(K, N)为底层图满足尖锐全局poincarcarve不等式提供了充分必要条件，该不等式转化为这些图的第一特征值的尖锐下界。圆锥曲率维数分析的另一个应用是找到完全图曲率的一个尖锐估计

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

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