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We study the long time behavior of the Hesse–Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse–Einstein metric. We also derive a convergence result for a twisted Hesse–Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse–Einstein metric by Cheng–Yau and Caffarelli–Viaclovsky as well as the real Calabi theorem by Cheng–Yau, Delanoë and Caffarelli–Viaclovsky.
@article{AIHPC_2023__40_6_1385_0,
author = {Puechmorel, St\'ephane and T\^o, Tat Dat},
title = {Convergence of the {Hesse{\textendash}Koszul} flow on compact {Hessian} manifolds},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1385--1414},
volume = {40},
number = {6},
year = {2023},
doi = {10.4171/aihpc/68},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/68/}
}
TY - JOUR AU - Puechmorel, Stéphane AU - Tô, Tat Dat TI - Convergence of the Hesse–Koszul flow on compact Hessian manifolds JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 1385 EP - 1414 VL - 40 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/68/ DO - 10.4171/aihpc/68 LA - en ID - AIHPC_2023__40_6_1385_0 ER -
%0 Journal Article %A Puechmorel, Stéphane %A Tô, Tat Dat %T Convergence of the Hesse–Koszul flow on compact Hessian manifolds %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 1385-1414 %V 40 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/68/ %R 10.4171/aihpc/68 %G en %F AIHPC_2023__40_6_1385_0
Puechmorel, Stéphane; Tô, Tat Dat. Convergence of the Hesse–Koszul flow on compact Hessian manifolds. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 6, pp. 1385-1414. doi: 10.4171/aihpc/68
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