Browse issues
no. 3
On the invariance of the total Monge–Ampère volume of Hermitian metrics
Ionuţ Chiose1
1 Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 575-579.

In this note, we describe the Hermitian metrics that leave the total Monge–Ampère volume invariant. In particular, we give several characterizations of the Hermitian metrics which satisfy the comparison principle for the complex Monge–Ampère operator.

Dans cette note, nous décrivons les métriques hermitiennes qui laissent le volume total de Monge–Ampère invariant, et nous donnons plusieurs caractérisations des métriques hermitiennes qui satisfont le principe de comparaison pour l’opérateur complexe de Monge–Ampère.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1781
Keywords: Hermitian metrics, Monge–Ampère operator, Comparison principle

Ionuţ Chiose 1

1 Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{AFST_2024_6_33_3_575_0,
     author = {Ionu\c{t} Chiose},
     title = {On the invariance of the total {Monge{\textendash}Amp\`ere} volume of {Hermitian} metrics},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {575--579},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 33},
     number = {3},
     year = {2024},
     doi = {10.5802/afst.1781},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1781/}
}
TY  - JOUR
AU  - Ionuţ Chiose
TI  - On the invariance of the total Monge–Ampère volume of Hermitian metrics
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2024
SP  - 575
EP  - 579
VL  - 33
IS  - 3
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1781/
DO  - 10.5802/afst.1781
LA  - en
ID  - AFST_2024_6_33_3_575_0
ER  - 
%0 Journal Article
%A Ionuţ Chiose
%T On the invariance of the total Monge–Ampère volume of Hermitian metrics
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2024
%P 575-579
%V 33
%N 3
%I Université Paul Sabatier, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1781/
%R 10.5802/afst.1781
%G en
%F AFST_2024_6_33_3_575_0
Ionuţ Chiose. On the invariance of the total Monge–Ampère volume of Hermitian metrics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 575-579. doi : 10.5802/afst.1781. https://afst.centre-mersenne.org/articles/10.5802/afst.1781/

[1] Daniele Angella; Vincent Guedj; Chinh H. Lu Plurisigned hermitian metrics, Trans. Amer. Math. Soc., Volume 376 (2023) no. 7, pp. 4631-4659 | DOI | Zbl

[2] Ionuţ Chiose Obstructions to the existence of Kähler structures on compact complex manifolds, Proc. Am. Math. Soc., Volume 142 (2014) no. 10, pp. 3561-3568 | DOI | Zbl

[3] Ionuţ Chiose The Kähler rank of compact complex manifolds, J. Geom. Anal., Volume 26 (2016) no. 1, pp. 603-615 | DOI | Zbl

[4] Sławomir Dinew Pluripotential theory on compact Hermitian manifolds, Ann. Fac. Sci. Toulouse, Math., Volume 25 (2016) no. 1, pp. 91-139 | DOI | Numdam | Zbl

[5] Sławomir Dinew; Vincent Guedj; Ahmed Zeriahi Open problems in pluripotential theory, Complex Var. Elliptic Equ., Volume 61 (2016) no. 7, pp. 902-930 | DOI | Zbl

[6] Sławomir Dinew; Sławomir Kołodziej Pluripotential estimates on compact Hermitian manifolds, Advances in geometric analysis (Advanced Lectures in Mathematics), Volume 21, International Press, 2012, pp. 69-86 | Zbl

[7] Bo Guan; Qun Li Complex Monge–Ampère equations and totally real submanifolds, Adv. Math., Volume 225 (2010) no. 3, pp. 1185-1223 | DOI | Zbl

[8] Vincent Guedj; Chinh H. Lu Quasi-plurisubharmonic envelopes 2: bounds on Monge–Ampère volumes, Algebr. Geom., Volume 9 (2022) no. 6, pp. 688-713 | DOI | Zbl

[9] Heisuke Hironaka An example of a non-Kählerian complex-analytic deformation of Kählerian complex structures, Ann. Math., Volume 75 (1962), pp. 190-208 | DOI | Zbl

Cited by Sources: