A new complete two-dimensional shrinking gradient K\"ahler-Ricci soliton

Richard H. Bamler; Charles Cifarelli; Ronan J. Conlon; Alix Deruelle

A new complete two-dimensional shrinking gradient K\"ahler-Ricci soliton

Differential Geometry 2022-06-23 v1

Authors: Richard H. Bamler , Charles Cifarelli , Ronan J. Conlon , Alix Deruelle

Abstract

We prove the existence of a unique complete shrinking gradient K\"ahler-Ricci soliton with bounded scalar curvature on the blowup of $\mathbb{C}\times\mathbb{P}^{1}$ at one point. This completes the classification of such solitons in two complex dimensions.

Keywords

kahler-ricci soliton shrinking gradient complex dimension two blowup scalar curvature

Cite

@article{arxiv.2206.10785,
  title  = {A new complete two-dimensional shrinking gradient K\"ahler-Ricci soliton},
  author = {Richard H. Bamler and Charles Cifarelli and Ronan J. Conlon and Alix Deruelle},
  journal= {arXiv preprint arXiv:2206.10785},
  year   = {2022}
}

Comments

11 pages

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