Experimental Evidence on Credit Constraints

Bando, Rosangela; Uribe, Claudia

doi:10.18235/0000252

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2017

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Cited by 1 publication

(2 citation statements)

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“…Remark. This argument follows an idea by Bando and Mabuchi in [1] to prove uniqueness of Kähler-Einstein metrics and it may be illuminating to compare the arguments. Bando and Mabuchi consider another perturbation defined by Aubin's continuity method which applies when [ω] = c 1 (X) and can be written…”

Section: Uniqueness Resultsmentioning

confidence: 96%

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Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics

Berman

Берндтссон

2017

J. Amer. Math. Soc.

119

192

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Abstract. 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 Käh-ler 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 homogenuous Monge-Ampère equation on a product domain, whose proof uses plurisubharmonic variation of Bergman kernels.

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Section: Uniqueness Resultsmentioning

confidence: 96%

“…In the case when [ω] = c 1 (X) this result is due to Bando-Mabuchi [1] while the case [ω] = c 1 (L) with Aut 0 (X) trivial was shown by Donaldson [27], using approximation with so called balanced metrics attached to high tensor powers of the line bundle L. The general uniqueness result appears in [22].…”

Section: Introductionmentioning

confidence: 87%