We prove that the image under any dominant meromorphic map of the Monge–Ampère measure of a Hölder continuous quasi-psh function still possesses a Hölder potential. We also discuss the case of lower regularity.
Nous démontrons que l’image par une application méromorphe dominante d’une mesure de Monge–Ampère d’une fonction quasi-psh et hölderienne possède aussi un potentiel hölderien. Nous discutons aussi le cas de régularité plus basse.
Classification: 32Q15, 32W20, 32Uxx
Keywords: Kähler manifolds, meromorphic map, Monge–Ampère measures
@article{AIF_2018__68_7_2965_0, author = {Di Nezza, Eleonora and Favre, Charles}, title = {Regularity of push-forward of {Monge{\textendash}Amp\`ere} measures}, journal = {Annales de l'Institut Fourier}, pages = {2965--2979}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {7}, year = {2018}, doi = {10.5802/aif.3233}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3233/} }
TY - JOUR TI - Regularity of push-forward of Monge–Ampère measures JO - Annales de l'Institut Fourier PY - 2018 DA - 2018/// SP - 2965 EP - 2979 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3233/ UR - https://doi.org/10.5802/aif.3233 DO - 10.5802/aif.3233 LA - en ID - AIF_2018__68_7_2965_0 ER -
Di Nezza, Eleonora; Favre, Charles. Regularity of push-forward of Monge–Ampère measures. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2965-2979. doi : 10.5802/aif.3233. https://aif.centre-mersenne.org/articles/10.5802/aif.3233/
[1] Representation Growth and Rational Singularities of the Moduli Space of Local Systems, Invent. Math., Tome 204 (2016) no. 1, pp. 245-316 | Zbl: 06581679
[2] The Dirichlet problem for the complex Monge-Ampère equation, Invent. Math., Tome 37 (1976), pp. 1-44 | Zbl: 0315.31007
[3] Monge–Ampère operators, Lelong numbers and intersection theory, Complex analysis and geometry (The University Series in Mathematics), Plenum Press, 1993 | Zbl: 0792.32006
[4] Hölder continuous solutions to Monge-Ampère equations, J. Eur. Math. Soc., Tome 16 (2014) no. 4, pp. 619-647 | Zbl: 1296.32012
[5] Stability of Monge–Ampère energy classes, J. Geom. Anal., Tome 25 (2014) no. 4, pp. 2565-2589 | Zbl: 1357.32024
[6] Finite Pluricomplex energy measures, Potential Anal., Tome 44 (2015) no. 1, pp. 155-167 | Zbl: 1357.32025
[7] Open problems in pluripotential theory, Complex Var. Elliptic Equ., Tome 61 (2016) no. 7, pp. 902-930 | Zbl: 1345.32040
[8] On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds, Adv. Math., Tome 225 (2010) no. 1, pp. 367-388 | Zbl: 1210.32020
[9] Characterization of Monge-Ampère measures with Hölder continuous potential, J. Funct. Anal., Tome 266 (2014), pp. 67-84
[10] Exponential estimates for plurisubharmonic functions and stochastic dynamics, J. Differ. Geom., Tome 84 (2010), pp. 465-488
[11] Degeneration of endomorphisms of the complex projective space in the hybrid space, J. Inst. Math. Jussieu (2018), 43 pages (43 p., published online) | Article
[12] Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal., Tome 15 (2005) no. 4, pp. 607-639
[13] The weighted Monge-Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal., Tome 250 (2007) no. 2, pp. 442-482
[14] Degenerate Complex Monge–Ampère Equations, EMS Tracts in Mathematics, Tome 26, Société Mathématique de France, 2017, xxiv+472 pages | Zbl: 1373.32001
[15] Hölder continuous solutions of the Monge-Ampère equation on compact hermitian manifolds, Ann. Inst. Fourier, Tome 68 (2018) no. 7, pp. 2951-2964
[16] Clôture intégrale des idéaux et équisingularité, Ann. Fac. Sci. Toulouse, Math., Tome 17 (2008) no. 4, pp. 781-859
[17] Modifications, Several complex variables VII: Sheaf theoretic methods in complex analysis (Encyclopaedia of Mathematical Sciences) Tome 74, Springer, 1994, pp. 285-317 | Zbl: 0807.32028
[18] Pushforwards of Measures on Real Varieties under Maps with Rational Singularities (2018) (https://arxiv.org/abs/1807.00079v1)
[19] Canonical measures and Kähler-Ricci flow, J. Am. Math. Soc., Tome 25 (2012) no. 2, pp. 303-353
[20] Adiabatic limits of Ricci-flat Kähler metrics, J. Differ. Geom., Tome 84 (2010) no. 2, pp. 427-453
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