Geodesic rays and stability in the cscK problem

By Chi Li. 2020

66 citations recorded by the source corpus.

We prove that any finite energy geodesic ray with a finite Mabuchi slope is maximal in the sense of Berman-Boucksom-Jonsson, and reduce the proof of the uniform Yau-Tian-Donaldson conjecture for constant scalar curvature Kahler metrics to Boucksom-Jonsson's regularization conjecture about the convergence of non-Archimedean entropy functional. As further applications, we show that a uniform K-stability condition for model filtrations and the $\mathcal{J}^{K_X}$-stability are both sufficient conditions for the existence of cscK metrics. The first condition is also conjectured to be necessary. Our arguments also produce a different proof of the toric uniform version of YTD conjecture for all polarized toric manifolds. Another result proved here is that the Mabuchi slope of a geodesic ray associated to a test configuration is equal to the non-Archimedean Mabuchi invariant.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/57b84521519429d76464edd522adf12d6621d0a0

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In Applied Mathematics

  1. Jiyuan Han
  2. Chi Li
  3. H. Blum
  4. Yuchen Liu
  5. Ziquan Zhuang
  6. Mattias Jonsson
  7. Xiaowei Wang
  8. Chenyang Xu

In Geometry and Topology

  1. Jiyuan Han
  2. Chi Li
  3. H. Blum
  4. Yuchen Liu
  5. Ziquan Zhuang
  6. Mattias Jonsson
  7. Xiaowei Wang
  8. Chenyang Xu

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