某些完全里奇孤子上漂移拉普拉斯特征值的估计

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2018-01-01 DOI:10.2206/KYUSHUJM.72.143

Lingzhong Zeng

{"title":"某些完全里奇孤子上漂移拉普拉斯特征值的估计","authors":"Lingzhong Zeng","doi":"10.2206/KYUSHUJM.72.143","DOIUrl":null,"url":null,"abstract":"Ricci solitons are the self-similar solutions to the Ricci flow, which play an important role in understanding the singularity dilations of the Ricci flow. In this paper, we investigate eigenvalues of the Dirichlet problem of a drifting Laplacian on some important complete Ricci solitons: the product shrinking Ricci soliton, cigar soliton, and so on. Since eigenvalues are invariant of isometries, we can give the estimates for the eigenvalues of a drifting Laplacian on the rotationally invariant shrinking solitons. In addition, we also obtain a sharp upper bound of the kth eigenvalue of the a drifting Laplacian on the product Ricci soliton in the sense of order k.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.143","citationCount":"9","resultStr":"{\"title\":\"ESTIMATES FOR THE EIGENVALUES OF THE DRIFTING LAPLACIAN ON SOME COMPLETE RICCI SOLITONS\",\"authors\":\"Lingzhong Zeng\",\"doi\":\"10.2206/KYUSHUJM.72.143\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ricci solitons are the self-similar solutions to the Ricci flow, which play an important role in understanding the singularity dilations of the Ricci flow. In this paper, we investigate eigenvalues of the Dirichlet problem of a drifting Laplacian on some important complete Ricci solitons: the product shrinking Ricci soliton, cigar soliton, and so on. Since eigenvalues are invariant of isometries, we can give the estimates for the eigenvalues of a drifting Laplacian on the rotationally invariant shrinking solitons. In addition, we also obtain a sharp upper bound of the kth eigenvalue of the a drifting Laplacian on the product Ricci soliton in the sense of order k.\",\"PeriodicalId\":49929,\"journal\":{\"name\":\"Kyushu Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.143\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kyushu Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2206/KYUSHUJM.72.143\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/KYUSHUJM.72.143","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 9

摘要

Ricci孤子是Ricci流的自相似解，它对理解Ricci流的奇异膨胀起着重要的作用。研究了一类重要的完全Ricci孤子(积缩Ricci孤子、雪茄孤子等)上漂移拉普拉斯算子Dirichlet问题的特征值。由于特征值在等距上是不变的，我们可以给出一个漂移拉普拉斯在旋转不变收缩孤子上的特征值的估计。此外，我们还得到了乘积Ricci孤子在k阶意义上的漂移拉普拉斯算子的第k个特征值的明显上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ESTIMATES FOR THE EIGENVALUES OF THE DRIFTING LAPLACIAN ON SOME COMPLETE RICCI SOLITONS

Ricci solitons are the self-similar solutions to the Ricci flow, which play an important role in understanding the singularity dilations of the Ricci flow. In this paper, we investigate eigenvalues of the Dirichlet problem of a drifting Laplacian on some important complete Ricci solitons: the product shrinking Ricci soliton, cigar soliton, and so on. Since eigenvalues are invariant of isometries, we can give the estimates for the eigenvalues of a drifting Laplacian on the rotationally invariant shrinking solitons. In addition, we also obtain a sharp upper bound of the kth eigenvalue of the a drifting Laplacian on the product Ricci soliton in the sense of order k.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.