{"title":"The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II)","authors":"Mingxiang Li","doi":"arxiv-2408.03640","DOIUrl":null,"url":null,"abstract":"This is a continuation of our previous work (Advances in Mathematics 450\n(2024), Paper No. 109768). In this paper, we characterize complete metrics with\nfinite total Q-curvature as normal metrics for all dimensional cases. Secondly,\nwe introduce another volume entropy to provide geometric information regarding\ncomplete non-normal metrics with finite total Q-curvature. In particular, we\nshow that if the scalar curvature is bounded from below, the volume growth of\nsuch complete metrics is controlled.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03640","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This is a continuation of our previous work (Advances in Mathematics 450
(2024), Paper No. 109768). In this paper, we characterize complete metrics with
finite total Q-curvature as normal metrics for all dimensional cases. Secondly,
we introduce another volume entropy to provide geometric information regarding
complete non-normal metrics with finite total Q-curvature. In particular, we
show that if the scalar curvature is bounded from below, the volume growth of
such complete metrics is controlled.
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