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

被引：0
|
作者：
Caldeira, Bruno [1 ]
Gentile, Giuseppe [2 ]
机构：
[1] Univ Fed Sao Carlos, Sao Carlos, Brazil
[2] Leibniz Univ Hannover, Hannover, Germany
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2024年 / 66卷 / 03期
关键词：
Phi-Manifolds; Bounded geometry; Heat kernel; Maximum principle; Schauder estimates;
D O I：
10.1007/s10455-024-09970-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：29
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