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Homogeneous Monge-Amp$\grave e$re Equations and Canonical Tubular Neighbourhoods in Kähler Geometry

dc.creatorRoss, Julius Andrew
dc.creatorNyström, David Witt
dc.date.accessioned2016-08-25
dc.date.accessioned2018-11-24T23:26:56Z
dc.date.available2016-10-25T13:14:36Z
dc.date.available2018-11-24T23:26:56Z
dc.date.issued2016
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/260896
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3918
dc.description.abstractWe prove the existence of canonical tubular neighbourhoods around complex submanifolds of Kähler manifolds that are adapted to both the holomorphic and symplectic structure. This is done by solving the complex Homogeneous Monge-Amp$\grave e$re equation on the deformation to the normal cone of the submanifold. We use this to establish local regularity for global weak solutions, giving local smoothness to the (weak) geodesic ray in the space of (weak) Kähler potentials associated to a given complex submanifold. We also use it to get an optimal regularity result for naturally defined plurisubharmonic envelopes and for the boundaries of their associated equilibrium sets.
dc.languageen
dc.publisherOxford University Press
dc.publisherInternational Mathematics Research Notices
dc.titleHomogeneous Monge-Amp$\grave e$re Equations and Canonical Tubular Neighbourhoods in Kähler Geometry
dc.typeArticle


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