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.
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.
Classification : 53C44, 32W20, 58J35
Mots clés : Monge–Ampère, stabilité, flot de Kähler–Ricci
@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 = {http://www.numdam.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 DA - 2018/// SP - 2819 EP - 2836 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3227/ UR - https://doi.org/10.5802/aif.3227 DO - 10.5802/aif.3227 LA - en ID - AIF_2018__68_7_2819_0 ER -
Guedj, Vincent; Lu, Chinh H.; Zeriahi, Ahmed. Stability of solutions to complex Monge–Ampère flows. Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2819-2836. doi : 10.5802/aif.3227. http://www.numdam.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 | Article | MR 0445006 | Zbl 0315.31007
[2] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982) no. 1-2, pp. 1-40 | Article | MR 674165
[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 | Article | MR 2021054
[4] Monge-Ampère equations in big cohomology classes, Acta Math., Volume 205 (2010) no. 2, pp. 199-262 | Article | MR 2746347
[5] Maximal subextensions of plurisubharmonic functions, Ann. Fac. Sci. Toulouse, Math., Volume 20 (2011) no. S2, pp. 101-122 | MR 2858169
[6] On the singularity type of full mass currents in big cohomology classes, Compos. Math., Volume 154 (2018) no. 2, pp. 380-409 | Article | MR 3738831 | Zbl 1398.32042
[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 | Article | MR 3089070
[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 | Article | MR 2669357
[10] Viscosity solutions to degenerate complex Monge-Ampère equations, Commun. Pure Appl. Math., Volume 64 (2011) no. 8, pp. 1059-1094 | Article | MR 2839271
[11] Weak solutions to degenerate complex Monge-Ampère flows II, Adv. Math., Volume 293 (2016), pp. 37-80 | Article | MR 3474319
[12] Stability of solutions to complex Monge-Ampère equations in big cohomology classes, Math. Res. Lett., Volume 19 (2012) no. 5, pp. 1025-1042 | Article | MR 3039828
[13] Degenerate complex Monge-Ampère equations, EMS Tracts in Mathematics, 26, European Mathematical Society, 2017, xxiv+472 pages | Article | MR 3617346
[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 | Article | MR 1414748 | Zbl 0878.32014
[15] The complex Monge-Ampère equation, Acta Math., Volume 180 (1998) no. 1, pp. 69-117 | Article | MR 1618325
[16] The Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J., Volume 52 (2003) no. 3, pp. 667-686 | Article | MR 1986892 | Zbl 1039.32050
[17] Weak solutions to the complex Hessian equation (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 | Article | MR 480350
Cité par Sources :