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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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1435-5345
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Volume 2015, Issue 700

Issues

Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature

Bobo Hua / Jürgen Jost
  • Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany; and Department of Mathematics and Computer Science, University of Leipzig, 04109 Leipzig, Germany
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/ Shiping Liu
  • Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany; and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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Published Online: 2013-04-11 | DOI: https://doi.org/10.1515/crelle-2013-0015

Abstract

We apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature. We obtain the metric classification of these graphs and construct the graphs embedded in the projective plane minus one point. Moreover, we show the volume doubling property and the Poincaré inequality on such graphs. The quadratic volume growth of these graphs implies the parabolicity. Finally, we prove the polynomial growth harmonic function theorem analogous to the case of Riemannian manifolds.

About the article

Received: 2011-07-20

Revised: 2013-02-01

Published Online: 2013-04-11

Published in Print: 2015-03-01


Funding Source: European Research Council

Award identifier / Grant number: 267087


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 700, Pages 1–36, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0015.

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Citing Articles

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[1]
Bobo Hua and Yanhui Su
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[2]
Matthias Keller and Michael Schwarz
Calculus of Variations and Partial Differential Equations, 2018, Volume 57, Number 2
[3]
Matthias Keller, Norbert Peyerimhoff, and Felix Pogorzelski
Advances in Mathematics, 2017, Volume 307, Page 1070
[4]
Bobo Hua and Yong Lin
Frontiers of Mathematics in China, 2016, Volume 11, Number 5, Page 1275
[5]
Frank Bauer, Bobo Hua, and Matthias Keller
Advances in Mathematics, 2013, Volume 248, Page 717

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