{"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}
引用次数: 0
Abstract
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.
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.
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