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Convexity of the K-...
Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics
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- Berman, Robert, 1976 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Berndtsson, Bo, 1950 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2017-03-02
- 2017
- Engelska.
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Ingår i: Journal of the American Mathematical Society. - : American Mathematical Society (AMS). - 0894-0347 .- 1088-6834. ; 30:4, s. 1165-1196
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Abstract
Ämnesord
Stäng
- We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kähler potentials on a compact Kähler manifold, thus confirming a conjecture of Chen, and give some applications in Kähler geometry, including a proof of the uniqueness of constant scalar curvature metrics (or more generally extremal metrics) modulo automorphisms. The key ingredient is a new local positivity property of weak solutions to the homogeneous Monge-Ampère equation on a product domain, whose proof uses plurisubharmonic variation of Bergman kernels.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- scalar curvature
- monge-ampere
- projective embeddings
- einstein metrics
- ricci solitons
- manifolds
- geometry
- stability
- existence
- geodesics
- Plurisubharmonic function
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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