Geodesic
Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains
Documenta mathematica, Tome 27 (2022), pp. 847-868 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Let π:Cn×C→C be the projection map onto the second factor and let D be a domain in Cn+1 such that for y∈π(D), every fiber Dy​:=D∩π−1(y) is a smoothly bounded strongly pseudoconvex domain in Cn and is diffeomorphic to each other. By Chau's theorem, the Kähler-Ricci flow has a long time solution ωy​(t) on each fiber Xy​. This family of flows induces a smooth real (1,1)-form ω(t) on the total space D whose restriction to the fiber Dy​ satisfies ω(t)∣Dy​​=ωy​(t). In this paper, we prove that ω(t) is positive for all t>0 in D if ω(0) is positive. As a corollary, we also prove that the fiberwise Kähler-Einstein metric is positive semi-definite on D if D is pseudoconvex in Cn+1.
DOI : 10.4171/dm/886
Classification : 32G05, 32T15, 53C55, 53E30
Mots-clés : positivity, Kähler-Einstein metric, Kähler-Ricci flow, fiberwise Kähler-Ricci flow, a family of strongly pseudoconvex domains 
@article{10_4171_dm_886,
     author = {Sungmin Yoo and Young-Jun Choi},
     title = {Fiberwise {K\"ahler-Ricci} flows on families of bounded strongly pseudoconvex domains},
     journal = {Documenta mathematica},
     pages = {847--868},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/886},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/886/}
}
TY  - JOUR
AU  - Sungmin Yoo
AU  - Young-Jun Choi
TI  - Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains
JO  - Documenta mathematica
PY  - 2022
SP  - 847
EP  - 868
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/886/
DO  - 10.4171/dm/886
ID  - 10_4171_dm_886
ER  - 
%0 Journal Article
%A Sungmin Yoo
%A Young-Jun Choi
%T Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains
%J Documenta mathematica
%D 2022
%P 847-868
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/886/
%R 10.4171/dm/886
%F 10_4171_dm_886
Sungmin Yoo; Young-Jun Choi. Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains. Documenta mathematica, Tome 27 (2022), pp. 847-868. doi: 10.4171/dm/886

Cité par Sources :