We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. This construction generalizes all previous known examples in the literature.
Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces / Pediconi, F; Sbiti, S. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - STAMPA. - 125:(2022), pp. 1130-1151. [10.1112/plms.12478]
Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces
Pediconi, F
;Sbiti, S
2022
Abstract
We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. This construction generalizes all previous known examples in the literature.
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