GRAPHS WITH NONNEGATIVE BAKRY-E<acute accent>MERY CURVATURE WITHOUT QUADRILATERAL

被引：0

作者：

Lin, Huiqiu ^{[1
]}

You, Zhe ^{[1
]}

机构：

[1] East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 153卷 / 05期

关键词：

Bakry-E<acute accent>mery curvature; C4-free graphs; curvature dimension condition; METRIC-MEASURE-SPACES; RICCI CURVATURE; INEQUALITY; GEOMETRY; GIRTH;

D O I：

10.1090/proc/17145

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The definition of Ricci curvature on graphs in Bakry-E<acute accent>mery's sense based on curvature dimension condition was introduced by Lin and Yau [Math. Res. Lett. 17 (2010), pp. 343-356]. Hua and Lin [Comm. Anal. Geom. 27 (2019), pp. 619-638] classified unweighted graphs satisfying the curvature dimension condition CD(0, infinity) whose girth are at least five. In this paper, we classify all of connected unweighted normalized C4-free graphs satisfying curvature dimension condition CD(0, infinity) for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition.

引用

页码：1839 / 1848

页数：10

共 23 条

[1]

Bakry D., 1985, Lectures Notes in Mathematics, V1123, P177

[2] The Graph Curvature Calculator and the Curvatures of Cubic Graphs [J].

Cushing, David ;

Kangaslampi, Riikka ;

Lipiainen, Valtteri ;

Liu, Shiping ;

Stagg, George W. .

EXPERIMENTAL MATHEMATICS, 2022, 31 (02) :583-595

[3] Curvatures, graph products and Ricci flatness [J].

Cushing, David ;

Kamtue, Supanat ;

Kangaslampi, Riikka ;

Liu, Shiping ;

Peyerimhoff, Norbert .

JOURNAL OF GRAPH THEORY, 2021, 96 (04) :522-553

[4] Quartic graphs which are Bakry-Emery curvature sharp [J].

Cushing, David ;

Kamtue, Supanat ;

Peyerimhoff, Norbert ;

May, Leyna Watson .

DISCRETE MATHEMATICS, 2020, 343 (03)

[5] Bakry-Emery Curvature Functions on Graphs [J].

Cushing, David ;

Liu, Shiping ;

Peyerimhoff, Norbert .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2020, 72 (01) :89-143

[6] Graphs with large girth and nonnegative curvature dimension condition [J].

Hua, Bobo ;

Lin, Yong .

COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2019, 27 (03) :619-638

[7] Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition [J].

Hua, Bobo .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (02)

[8] Stochastic completeness for graphs with curvature dimension conditions [J].

Hua, Bobo ;

Lin, Yong .

ADVANCES IN MATHEMATICS, 2017, 306 :279-302

[9] Ollivier's Ricci Curvature, Local Clustering and Curvature-Dimension Inequalities on Graphs [J].

Jost, Juergen ;

Liu, Shiping .

DISCRETE & COMPUTATIONAL GEOMETRY, 2014, 51 (02) :300-322

[10] Discrete Curvature and Abelian Groups [J].

Klartag, Bo'az ;

Kozma, Gady ;

Ralli, Peter ;

Tetali, Prasad .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2016, 68 (03) :655-674

← 1 2 3 →