Comparison of Monge-Ampère capacities

Lu, Chinh H.

doi:10.48550/arxiv.2005.04264

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Radial Functionals In Terms Of Legendre Transforms1

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2020

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“…This result is well-known when ψ and ϕ are smooth. In general, it follows from a direct computation using integration by parts ([Xia19], [Lu20]).…”

Section: Radial Functionals In Terms Of Legendre Transformsmentioning

confidence: 99%

Pluripotential-theoretic stability thresholds

Xia¹

2020

Preprint

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Given a compact polarized manifold (X, L), we introduce two new stability thresholds in terms of singularity types of global quasi-plurisubharmonic functions on X. We prove that in the Fano setting, the new invariants can effectively detect the K-stability of X. We study some functionals of geodesic rays in the space of Kähler potentials by means of the corresponding test curves. In particular, we introduce a new entropy functional of quasi-plurisubharmonic functions and relate the radial entropy functional to this new entropy functional.

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“…This result is well-known when ψ and ϕ are smooth. In general, it follows from a direct computation using integration by parts ([Xia19], [Lu20]).…”

Section: Radial Functionals In Terms Of Legendre Transformsmentioning

confidence: 99%