| 1. |
- Boucksom, Sebastien, et al.
(författare)
-
Uniform K-stability and asymptotics of energy functionals in Kähler geometry
- 2019
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Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 21:9, s. 2905-2944
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Tidskriftsartikel (refereegranskat)abstract
- Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X, L). For many common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper [BHJ17]) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability, as defined in [Der15, BHJ17]. As a partial converse, we show that uniform K-stability implies coercivity of the Mabuchi functional when restricted to Bergman metrics.
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| 2. |
- Boucksom, S., et al.
(författare)
-
Uniform K-stability and asymptotics of energy functionals in Kähler geometry
- 2019
-
Ingår i: Journal of the European Mathematical Society. - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855. ; 21:9, s. 2905-2944
-
Tidskriftsartikel (refereegranskat)abstract
- Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X, L). For many common functionals in Kahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper [BHJ17]) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability, as defined in [Der 15, BHJ17]. As a partial converse, we show that uniform K-stability implies coercivity of the Mabuchi functional when restricted to Bergman metrics.
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