Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem
DC Field | Value | Language |
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dc.contributor.author | Oh, Byung Geun | - |
dc.date.accessioned | 2022-07-06T10:30:53Z | - |
dc.date.available | 2022-07-06T10:30:53Z | - |
dc.date.created | 2021-07-15 | - |
dc.date.issued | 2022-02 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/139682 | - |
dc.description.abstract | We investigate criteria for circle packing (CP) types of disk triangulation graphs embedded into simply connected domains in C. In particular, by studying combinatorial curvature and the combinatorial Gauss-Bonnet theorem involving boundary turns, we show that a disk triangulation graph is CP parabolic if Sigma(infinity)(n=1) 1/Sigma(n-1)(j=0) (k(j) + 6) = infinity, where k(n) is the degree excess sequence defined by k(n) = Sigma(v)(is an element of Bn) (deg v - 6) for combinatorial balls B-n of radius n and centered at a fixed vertex. It is also shown that the simple random walk on a disk triangulation graph is recurrent if Sigma(infinity)(n=1) 1/Sigma(n-1)(j=0) (k(j) + 6) + Sigma(n)(j=0) (k(j) + 6) = infinity. These criteria are sharp, and generalize a conjecture by He and Schramm in their paper from 1995, which was later proved by Repp in 2001. We also give several criteria for CP hyperbolicity, one of which generalizes a theorem of He and Schramm, and present a necessary and sufficient condition for CP types of layered circle packings generalizing and confirming a criterion given by Siders in 1998. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.title | Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Oh, Byung Geun | - |
dc.identifier.doi | 10.1090/tran/8503 | - |
dc.identifier.scopusid | 2-s2.0-85124604150 | - |
dc.identifier.wosid | 000749154300001 | - |
dc.identifier.bibliographicCitation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.375, no.2, pp.753 - 797 | - |
dc.relation.isPartOf | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.title | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 375 | - |
dc.citation.number | 2 | - |
dc.citation.startPage | 753 | - |
dc.citation.endPage | 797 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | PLANAR | - |
dc.subject.keywordPlus | CURVATURE | - |
dc.subject.keywordPlus | FORMULA | - |
dc.subject.keywordPlus | GRAPHS | - |
dc.subject.keywordPlus | VERTICES | - |
dc.subject.keywordPlus | TILINGS | - |
dc.subject.keywordPlus | ANALOG | - |
dc.identifier.url | https://www.ams.org/journals/tran/2022-375-02/S0002-9947-2021-08503-7/ | - |
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