Stability and integration over Bergman metrics

@article{Klevtsov2014StabilityAI,
  title={Stability and integration over Bergman metrics},
  author={Semyon Klevtsov and Steve Zelditch},
  journal={Journal of High Energy Physics},
  year={2014},
  volume={2014},
  pages={1-27}
}
A bstractWe study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as ‘stability functions’. We introduce a new stability invariant — the critical value of the coupling constant — defined as the minimal coupling constant for which the partition function converges. It measures the minimal degree of stability of geodesic rays in the space the Bergman metrics, with respect to the action. We calculate this critical value when the… 
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12 Citations
Background Citations
7
Methods Citations
2

12 Citations

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We derive an explicit formula for the asymptotic slope of the Aubin–Yau functional along a Bergman geodesic on a surface of complex dimension 2, extending the work of Phong–Sturm (On asymptotics for…

Asymptotic Slopes of the Aubin–Yau Functional and Calculation of the Donaldson–Futaki Invariant

  • D. Rubin
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    The Journal of Geometric Analysis
  • 2017
We derive an explicit formula for the asymptotic slope of the Aubin–Yau functional along a Bergman geodesic on a surface of complex dimension 2, extending the work of Phong–Sturm (On asymptotics for…

Ju l 2 01 7 ASYMPTOTIC SLOPES OF THE AUBIN-YAU FUNCTIONAL

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