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We construct many new examples of complete Calabi-Yau metrics of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones with smooth cross-sections. A detailed description of the geometry at infinity of these metrics is given in terms of a compactification by a manifold with corners obtained through the notion of weighted blow-up for manifolds with corners. A key analytical step in the construction of these Calabi-Yau metrics is to derive good mapping properties of the Laplacian on some suitable weighted Hölder spaces.
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Products of manifolds with fibered corners
Manifolds with fibered corners arise as resolutions of stratified spaces, as ‘many-body’ compactifications of vector spaces, and as compactifications of certain moduli spaces includ- ing those of non-abelian Yang–Mills–Higgs monopoles, among other settings. However, Cartesian products of manifolds with fibered corners do not generally have fibered corners themselves and thus fail to reflect the appropriate structure of products of the underlying spaces in the above settings. Here, we determine a resolution of the Cartesian product of fibered corners manifolds by blow-up which we call the ‘ordered product,’ which leads to a well-behaved category of fibered corners manifolds in which the ordered product satisfies the appropriate universal property. In contrast to the usual category of manifolds with cor- ners, this category of fibered corners not only has all finite products, but all finite transverse fiber products as well, and we show in addition that the ordered product is a natural product for wedge (aka incomplete edge) metrics and quasi-fibered boundary metrics, a class which includes QAC and QALE metrics.
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- Award ID(s):
- 1811995
- PAR ID:
- 10554525
- Publisher / Repository:
- Springer Nature B.V.
- Date Published:
- Journal Name:
- Annals of Global Analysis and Geometry
- Volume:
- 64
- Issue:
- 2
- ISSN:
- 0232-704X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10455-023-09912-1
