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Geodesics in the space of Kähler cone metrics, I
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Calamai, Simone and Zheng, Kai (2015) Geodesics in the space of Kähler cone metrics, I. American Journal of Mathematics , 137 (5). pp. 1149-1208.
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Abstract
In this paper, we study the Dirichlet problem of the geodesic equation in the space of Kähler cone metrics Hβ ; that is equivalent to a homogeneous complex Monge–Ampère equation whose boundary values consist of Kähler metrics with cone sin- gularities. Our approach concerns the generalization of the function space defined in Donaldson [25] to the case of Kähler manifolds with boundary; moreover we introduce a subspace HC of Hβ which we define by prescribing appropriate geometric conditions. Our main result is the existence, uniqueness and regularity of Cβ1’1 geodesics whose boundary values lie in HC. Moreover, we prove that such geodesic is the limit of a sequence of Cβ2’α approximate geodesics under the Cβ1’1 -norm. As a geometric application, we prove the metric space structure of HC.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Kählerian manifolds, Homogeneous complex manifolds | ||||||||||||||||||
| Journal or Publication Title: | American Journal of Mathematics | ||||||||||||||||||
| Publisher: | The Johns Hopkins University Press | ||||||||||||||||||
| ISSN: | 0002-9327 | ||||||||||||||||||
| Official Date: | October 2015 | ||||||||||||||||||
| Dates: |
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| Volume: | 137 | ||||||||||||||||||
| Number: | 5 | ||||||||||||||||||
| Page Range: | pp. 1149-1208 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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