有纤维边界流形上的热型方程 I：绍德估计

IF 0.6 3区数学 Q3 MATHEMATICS Annals of Global Analysis and Geometry Pub Date : 2024-09-26 DOI:10.1007/s10455-024-09970-z

Bruno Caldeira, Giuseppe Gentile

{"title":"有纤维边界流形上的热型方程 I：绍德估计","authors":"Bruno Caldeira, Giuseppe Gentile","doi":"10.1007/s10455-024-09970-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold <i>M</i> with fibered boundary and a <span>\\(\\Phi \\)</span>-metric <span>\\(g_\\Phi \\)</span>. This setting generalizes the asymptotically conical (scattering) spaces and includes special cases of gravitational instantons. This paper, combined with part II, lay the crucial groundwork for forthcoming discussions on geometric flows in this setting; especially the Yamabe- and mean curvature flow.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Heat-type equations on manifolds with fibered boundaries I: Schauder estimates\",\"authors\":\"Bruno Caldeira, Giuseppe Gentile\",\"doi\":\"10.1007/s10455-024-09970-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold <i>M</i> with fibered boundary and a <span>\\\\(\\\\Phi \\\\)</span>-metric <span>\\\\(g_\\\\Phi \\\\)</span>. This setting generalizes the asymptotically conical (scattering) spaces and includes special cases of gravitational instantons. This paper, combined with part II, lay the crucial groundwork for forthcoming discussions on geometric flows in this setting; especially the Yamabe- and mean curvature flow.</p></div>\",\"PeriodicalId\":8268,\"journal\":{\"name\":\"Annals of Global Analysis and Geometry\",\"volume\":\"66 3\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Global Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10455-024-09970-z\",\"RegionNum\":3,\"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":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-024-09970-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们证明了具有纤维边界和 \(\Phi \)度量 \(g_\Phi \)的流形 M 上的拉普拉斯-贝尔特拉米算子的抛物线 Schauder 估计。这种设置概括了渐近圆锥（散射）空间，并包括引力瞬子的特殊情况。本文与第二部分相结合，为即将讨论这种环境下的几何流奠定了重要基础；特别是山叶流和平均曲率流。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Heat-type equations on manifolds with fibered boundaries I: Schauder estimates

In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold M with fibered boundary and a \(\Phi \)-metric \(g_\Phi \). This setting generalizes the asymptotically conical (scattering) spaces and includes special cases of gravitational instantons. This paper, combined with part II, lay the crucial groundwork for forthcoming discussions on geometric flows in this setting; especially the Yamabe- and mean curvature flow.

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.

期刊最新文献

Coclosed \(G_2\)-structures on \(\text {SU}(2)^2\)-invariant cohomogeneity one manifolds Generalized positive scalar curvature on spin\(^c\) manifolds A critical perturbation result in prescribing scalar curvature under boundary conditions The zeta-determinant of the Dirichlet-to-Neumann operator on forms On the Gromov–Hausdorff limits of compact surfaces with boundary