Rotational symmetry of complete shrinking gradient Yamabe solitons
Differential Geometry
2026-04-07 v5
Abstract
In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally symmetric. This assumption is optimal for higher dimensions. This result resolves the Yamabe-soliton analogue of Perelman's conjecture.
Keywords
Cite
@article{arxiv.2309.09166,
title = {Rotational symmetry of complete shrinking gradient Yamabe solitons},
author = {Shun Maeta},
journal= {arXiv preprint arXiv:2309.09166},
year = {2026}
}
Comments
10 pages