Continuity method for the Mabuchi soliton on the extremal Fano manifolds
Differential Geometry
2025-05-20 v2
Abstract
We run the continuity method for Mabuchi's generalization of K\"{a}hler-Einstein metrics, assuming the existence of an extremal K\"{a}hler metric. It gives an analytic proof (without minimal model program) of the recent existence result obtained by Apostolov, Lahdili and Nitta. Our key observation is the boundedness of the energy functionals along the continuity method. The same argument can be applied to general -solitons and -extremal metrics.
Keywords
Cite
@article{arxiv.2409.00886,
title = {Continuity method for the Mabuchi soliton on the extremal Fano manifolds},
author = {Tomoyuki Hisamoto and Satoshi Nakamura},
journal= {arXiv preprint arXiv:2409.00886},
year = {2025}
}
Comments
19 pages. The weight functions for $g$-solitons are assumed to be log-concave. Final version, to appear in Ann. Inst. Fourier (Grenoble)