Journal of the American Mathematical Society· 2014Q1
Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
- 390citations
- Q1SCImago
- 2014year
Short summary
A sequence of smooth Kähler metrics can approximate Kähler-Einstein metrics with cone singularities on Fano manifolds in the Gromov-Hausdorff sense.
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Key points
- Introduces a sequence of smooth Kähler metrics.
- These metrics approximate Kähler-Einstein metrics with cone singularities.
- The approximation is demonstrated in the Gromov-Hausdorff sense.
- This work is the first in a series proving K-stable Fano manifolds admit Kähler-Einstein metrics.
AI-generated from the title and abstract; the full text is not read.
Abstract
This is the first of a series of three papers which prove the fact that a <italic>K</italic> -stable Fano manifold admits a Kähler-Einstein metric. The main result of this paper is that a Kähler-Einstein metric with cone singularities along a divisor can be approximated by a sequence of smooth Kähler metrics with controlled geometry in the Gromov-Hausdorff sense.
The authors' abstract, as published at the source. Journal of the American Mathematical Society, 2014 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics