Details
| Original language | English |
|---|---|
| Article number | 12 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 66 |
| Issue number | 3 |
| Early online date | 26 Sept 2024 |
| Publication status | Published - Oct 2024 |
Abstract
In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold M with fibered boundary and a Φ-metric gΦ. 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.
Keywords
- Bounded geometry, Heat kernel, Maximum principle, Schauder estimates, Φ-Manifolds
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Geometry and Topology
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In: Annals of Global Analysis and Geometry, Vol. 66, No. 3, 12, 10.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Heat-type equations on manifolds with fibered boundaries I
T2 - Schauder estimates
AU - Caldeira, Bruno
AU - Gentile, Giuseppe
N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature B.V. 2024.
PY - 2024/10
Y1 - 2024/10
N2 - In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold M with fibered boundary and a Φ-metric gΦ. 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.
AB - In this paper, we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold M with fibered boundary and a Φ-metric gΦ. 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.
KW - Bounded geometry
KW - Heat kernel
KW - Maximum principle
KW - Schauder estimates
KW - Φ-Manifolds
UR - http://www.scopus.com/inward/record.url?scp=85204927306&partnerID=8YFLogxK
U2 - 10.1007/s10455-024-09970-z
DO - 10.1007/s10455-024-09970-z
M3 - Article
AN - SCOPUS:85204927306
VL - 66
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 3
M1 - 12
ER -