Regularity of push-forward of Monge–Ampère measures  [ Régularité par poussé en avant des mesures de Monge–Ampère ]
Annales de l'Institut Fourier, à paraître, 15 p.

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.

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.

Publié le : 2019-03-08
Classification:  32Q15,  32W20,  32Uxx
Mots clés: variétés kähleriennes, application méromorphe, mesures de Monge–Ampère
@unpublished{AIF_0__0_0_A41_0,
     author = {Di Nezza, Eleonora and Favre, Charles},
     title = {Regularity of push-forward of Monge--Amp\`ere measures},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Di Nezza, Eleonora; Favre, Charles. Regularity of push-forward of Monge–Ampère measures. Annales de l'Institut Fourier, à paraître, 15 p.

[1] Aizenbud, Avraham; Avni, Nir 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] Bedford, Eric; Taylor, Bert A. The Dirichlet problem for the complex Monge-Ampère equation, Invent. Math., Tome 37 (1976), pp. 1-44 | Zbl 0315.31007

[3] Demailly, Jean-Pierre Monge–Ampère operators, Lelong numbers and intersection theory, Complex analysis and geometry, Plenum Press (The University Series in Mathematics) (1993) | Zbl 0792.32006

[4] Demailly, Jean-Pierre; Dinew, Sławomir; Guedj, Vincent; Hiep, Pham Hoang; Kołodziej, Sławomir; Zeriahi, Ahmed Hölder continuous solutions to Monge-Ampère equations, J. Eur. Math. Soc., Tome 16 (2014) no. 4, pp. 619-647 | Zbl 1296.32012

[5] Di Nezza, Eleonora Stability of Monge–Ampère energy classes, J. Geom. Anal., Tome 25 (2014) no. 4, pp. 2565-2589 | Zbl 1357.32024

[6] Di Nezza, Eleonora Finite Pluricomplex energy measures, Potential Anal., Tome 44 (2015) no. 1, pp. 155-167 | Zbl 1357.32025

[7] Dinew, Sławomir; Guedj, Vincent; Zeriahi, Ahmed Open problems in pluripotential theory, Complex Var. Elliptic Equ., Tome 61 (2016) no. 7, pp. 902-930 | Zbl 1345.32040

[8] Dinew, Sławomir; Zhang, Zhou 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] Dinh, Tien Cuong; Nguyen, Viet Anh Characterization of Monge-Ampère measures with Hölder continuous potential, J. Funct. Anal., Tome 266 (2014), pp. 67-84

[10] Dinh, Tien Cuong; Nguyen, Viet Anh; Sibony, Nessim Exponential estimates for plurisubharmonic functions and stochastic dynamics, J. Differ. Geom., Tome 84 (2010), pp. 465-488

[11] Favre, Charles 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] Guedj, Vincent; Zeriahi, Ahmed Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal., Tome 15 (2005) no. 4, pp. 607-639

[13] Guedj, Vincent; Zeriahi, Ahmed The weighted Monge-Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal., Tome 250 (2007) no. 2, pp. 442-482

[14] Guedj, Vincent; Zeriahi, Ahmed Degenerate Complex Monge–Ampère Equations, Société Mathématique de France, EMS Tracts in Mathematics, Tome 26 (2017), xxiv+472 pages | Zbl 1373.32001

[15] Kołodziej, Sławomir; Nguyen, Ngoc Cuong Hölder continuous solutions of the Monge-Ampère equation on compact hermitian manifolds, Ann. Inst. Fourier, Tome TBD (TBD) no. TBD

[16] Lejeune-Jalabert, Monique; Teissier, Bernard; Risler, Jean-Jacques Clôture intégrale des idéaux et équisingularité, Ann. Fac. Sci. Toulouse, Math., Tome 17 (2008) no. 4, pp. 781-859

[17] Peternell, Thomas Modifications, Several complex variables VII: Sheaf theoretic methods in complex analysis, Springer (Encyclopaedia of Mathematical Sciences) Tome 74 (1994), pp. 285-317 | Zbl 0807.32028

[18] Reiser, Andrew Pushforwards of Measures on Real Varieties under Maps with Rational Singularities (2018) (https://arxiv.org/abs/1807.00079v1 )

[19] Song, Jian; Tian, Gang Canonical measures and Kähler-Ricci flow, J. Am. Math. Soc., Tome 25 (2012) no. 2, pp. 303-353

[20] Tosatti, Valentino Adiabatic limits of Ricci-flat Kähler metrics, J. Differ. Geom., Tome 84 (2010) no. 2, pp. 427-453