English

Two-dimensional gradient Ricci solitons revisited

Differential Geometry 2015-03-26 v2

Abstract

In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded curvature. Second, we give examples of complete two-dimensional expanding Ricci solitons with negative curvature that are topologically disks and are not hyperbolic space.

Keywords

Cite

@article{arxiv.1303.6854,
  title  = {Two-dimensional gradient Ricci solitons revisited},
  author = {Jacob Bernstein and Thomas Mettler},
  journal= {arXiv preprint arXiv:1303.6854},
  year   = {2015}
}

Comments

15 pages, 3 figures. Corrected statement and proof of Theorem 2 and removed Corollary 1

R2 v1 2026-06-21T23:49:10.364Z