We establish a stability result for elliptic and parabolic complex Monge–Ampère equations on compact Kähler manifolds, which applies in particular to the Kähler–Ricci flow.
Nous établissons un résultat de stabilité pour les équations de Monge–Ampère complexes elliptiques et paraboliques sur les variétés Kähleriennes compactes, qui s’appliquent en particulier au flot de Kähler–Ricci.
Keywords: Monge–Ampère, stability, Kähler–Ricci flow
Mot clés : Monge–Ampère, stabilité, flot de Kähler–Ricci
Guedj, Vincent 1; Lu, Chinh H. 2; Zeriahi, Ahmed 1
@article{AIF_2018__68_7_2819_0, author = {Guedj, Vincent and Lu, Chinh H. and Zeriahi, Ahmed}, title = {Stability of solutions to complex {Monge{\textendash}Amp\`ere} flows}, journal = {Annales de l'Institut Fourier}, pages = {2819--2836}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {7}, year = {2018}, doi = {10.5802/aif.3227}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3227/} }
TY - JOUR AU - Guedj, Vincent AU - Lu, Chinh H. AU - Zeriahi, Ahmed TI - Stability of solutions to complex Monge–Ampère flows JO - Annales de l'Institut Fourier PY - 2018 SP - 2819 EP - 2836 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3227/ DO - 10.5802/aif.3227 LA - en ID - AIF_2018__68_7_2819_0 ER -
%0 Journal Article %A Guedj, Vincent %A Lu, Chinh H. %A Zeriahi, Ahmed %T Stability of solutions to complex Monge–Ampère flows %J Annales de l'Institut Fourier %D 2018 %P 2819-2836 %V 68 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3227/ %R 10.5802/aif.3227 %G en %F AIF_2018__68_7_2819_0
Guedj, Vincent; Lu, Chinh H.; Zeriahi, Ahmed. Stability of solutions to complex Monge–Ampère flows. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2819-2836. doi : 10.5802/aif.3227. https://aif.centre-mersenne.org/articles/10.5802/aif.3227/
[1] The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math., Volume 37 (1976) no. 1, pp. 1-44 | DOI | MR | Zbl
[2] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982) no. 1-2, pp. 1-40 | DOI | MR
[3] Uniqueness and stability for the complex Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J., Volume 52 (2003) no. 6, pp. 1697-1701 | DOI | MR
[4] Monge-Ampère equations in big cohomology classes, Acta Math., Volume 205 (2010) no. 2, pp. 199-262 | DOI | MR
[5] Maximal subextensions of plurisubharmonic functions, Ann. Fac. Sci. Toulouse, Math., Volume 20 (2011) no. S2, pp. 101-122 | MR
[6] On the singularity type of full mass currents in big cohomology classes, Compos. Math., Volume 154 (2018) no. 2, pp. 380-409 | DOI | MR | Zbl
[7] Potential Theory In Several Complex Variables, 1989 (Course of the author at the ICPAM Summer School on Complex Analysis, Nice, France, July 3–7, available at https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/nice_cimpa.pdf)
[8] Applications of pluripotential theory to algebraic geometry, Pluripotential theory (Lecture Notes in Mathematics), Volume 2075, Springer, 2013, pp. 143-263 | DOI | MR
[9] On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds, Adv. Math., Volume 225 (2010) no. 1, pp. 367-388 | DOI | MR
[10] Viscosity solutions to degenerate complex Monge-Ampère equations, Commun. Pure Appl. Math., Volume 64 (2011) no. 8, pp. 1059-1094 | DOI | MR
[11] Weak solutions to degenerate complex Monge-Ampère flows II, Adv. Math., Volume 293 (2016), pp. 37-80 | DOI | MR
[12] Stability of solutions to complex Monge-Ampère equations in big cohomology classes, Math. Res. Lett., Volume 19 (2012) no. 5, pp. 1025-1042 | DOI | MR
[13] Degenerate complex Monge-Ampère equations, EMS Tracts in Mathematics, 26, European Mathematical Society, 2017, xxiv+472 pages | DOI | MR
[14] Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator, Ann. Pol. Math., Volume 65 (1996) no. 1, pp. 11-21 | DOI | MR | Zbl
[15] The complex Monge-Ampère equation, Acta Math., Volume 180 (1998) no. 1, pp. 69-117 | DOI | MR
[16] The Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J., Volume 52 (2003) no. 3, pp. 667-686 | DOI | MR | Zbl
[17] Weak solutions to the complex Hessian equation, Jagiellonian University (Poland) (2014) (Ph. D. Thesis)
[18] On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Commun. Pure Appl. Math., Volume 31 (1978) no. 3, pp. 339-411 | DOI | MR
Cited by Sources: