Charabati, Mohamad; Zeriahi, Ahmed The continuous subsolution problem for complex Hessian equations. (English) Zbl 07978142 Indiana Univ. Math. J. 73, No. 5, 1639-1688 (2024). MSC: 31C45 32U15 32U40 32W20 35J66 35J96 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Ngoc Cuong Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds. (English) Zbl 07935729 Trans. Am. Math. Soc. 377, No. 11, 8091-8123 (2024). MSC: 32U35 32Q15 32V20 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tang Van Long; Nguyen Xuan Hong; Pham Thi Lieu Continuity of the Perron-Bremermann envelope of plurisubharmonic functions. (English) Zbl 1548.32055 Collect. Math. 75, No. 3, 659-670 (2024). MSC: 32U05 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyen Van Trao; Nguyen Xuan Hong; Pham Nguyen Thu Trang Hölder continuity of solutions of the Dirichlet problem in pseudoconvex domains. (English) Zbl 07915210 Complex Var. Elliptic Equ. 69, No. 9, 1523-1536 (2024). MSC: 32W20 32T99 × Cite Format Result Cite Review PDF Full Text: DOI
Le Mau Hai; Pham Hoang Hiep; Trinh Tung Cone of maximal subextensions of the plurisubharmonic functions. (English) Zbl 07872378 Acta Math. Vietnam. 49, No. 1, 83-97 (2024). Reviewer: Rafał Czyż (Kraków) MSC: 32U05 32U15 32U25 32U40 32W20 × Cite Format Result Cite Review PDF Full Text: DOI
Guedj, Vincent; Guenancia, Henri; Zeriahi, Ahmed Strict positivity of Kähler-Einstein currents. (English) Zbl 1546.32008 Forum Math. Sigma 12, Paper No. e68, 27 p. (2024). Reviewer: Masaya Kawamura (Nagoya) MSC: 32Q20 14B05 32Q25 32S30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Jiaxiang; Zhou, Bin Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations. (English) Zbl 1537.32125 Sci. China, Math. 67, No. 3, 557-576 (2024). MSC: 32U05 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amal, Hichame; Asserda, Saïd; Bouhssina, Manar Hölder continuity for solutions of the complex Hessian type equation. (English) Zbl 1531.32041 Rend. Circ. Mat. Palermo (2) 73, No. 1, 267-289 (2024). MSC: 32U05 32W50 32T99 × Cite Format Result Cite Review PDF Full Text: DOI
Badiane, Papa; Zeriahi, Ahmed The eigenvalue problem for the complex Monge-Ampère operator. (English) Zbl 1530.32017 J. Geom. Anal. 33, No. 12, Paper No. 367, 44 p. (2023). Reviewer: Marek Jarnicki (Kraków) MSC: 32U05 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pan, Chung-Ming Families of singular Chern-Ricci flat metrics. (English) Zbl 1509.14024 J. Geom. Anal. 33, No. 2, Paper No. 66, 32 p. (2023). Reviewer: Yang Li (Cambridge) MSC: 14D06 32Q25 32U05 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kołodziej, Sławomir; Nguyen, Ngoc Cuong The Dirichlet problem for the Monge-Ampère equation on Hermitian manifolds with boundary. (English) Zbl 1517.32122 Calc. Var. Partial Differ. Equ. 62, No. 1, Paper No. 1, 39 p. (2023). Reviewer: Emil J. Straube (College Station) MSC: 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kołodziej, Sławomir; Nguyen, Ngoc Cuong Weak solutions to Monge-Ampère type equations on compact Hermitian manifold with boundary. (English) Zbl 1531.32045 J. Geom. Anal. 33, No. 1, Paper No. 15, 20 p. (2023). Reviewer: Rafał Czyż (Kraków) MSC: 32U40 32W20 53C55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinh, Tien-Cuong; Kołodziej, Sławomir; Nguyen, Ngoc Cuong The complex Sobolev space and Hölder continuous solutions to Monge-Ampère equations. (English) Zbl 1522.32085 Bull. Lond. Math. Soc. 54, No. 2, 772-790 (2022). MSC: 32W20 32J27 46E35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pham Nguyen Thu Trang; Nguyen Duc Hung; Nguyen Xuan Hong Envelope of plurisubharmonic functions in Cegrell’s classes. (English) Zbl 1504.32089 Anal. Math. Phys. 12, No. 6, Paper No. 138, 13 p. (2022). MSC: 32U05 32W20 × Cite Format Result Cite Review PDF Full Text: DOI
Vu Van Quan Continuous solutions to the complex \(m\)-Hessian type equation on strongly \(m\)-pseudoconvex domains in \(\mathbb{C}^n\). (English) Zbl 1487.32180 Result. Math. 77, No. 3, Paper No. 127, 13 p. (2022). MSC: 32U05 32U15 32U40 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyen Xuan Hong; Pham Thi Lieu Local Hölder continuity of solutions of the complex Monge-Ampère equation. (English) Zbl 1478.32125 J. Math. Anal. Appl. 507, No. 1, Article ID 125737, 8 p. (2022). MSC: 32W20 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lu, Chinh H.; Phung, Trong-Thuc; Tô, Tât-Dat Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds. (Stabilité et continuité Höldérienne des solutions des équations de Monge-Ampère complexes sur des variétés hermitiennes compactes.) (English. French summary) Zbl 1487.32207 Ann. Inst. Fourier 71, No. 5, 2019-2045 (2021). MSC: 32W20 32U05 32Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Le Mau Hai; Vu Van Quan Existence and Hölder continuity to solutions of the complex Monge-Ampère-type equations with measures vanishing on pluripolar subsets. (English) Zbl 1487.32205 Int. J. Math. 32, No. 14, Article ID 2150099, 19 p. (2021). MSC: 32W20 32T15 35B65 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Jia Xiang; Zhou, Bin Regularity for a class of singular complex Hessian equations. (English) Zbl 1484.32054 Acta Math. Sin., Engl. Ser. 37, No. 11, 1709-1720 (2021). MSC: 32W20 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyen Xuan Hong; Pham Thi Lieu The Dirichlet problem for the complex Monge-Ampère operator on strictly plurifinely pseudoconvex domains. (English) Zbl 1478.32108 Complex Anal. Oper. Theory 15, No. 8, Paper No. 124, 11 p. (2021). MSC: 32U05 32U15 32U40 × Cite Format Result Cite Review PDF Full Text: DOI
Hung, V. V.; Quy, H. N. A remark on covering of compact Kähler manifolds and applications. (English) Zbl 1478.32124 Ukr. Math. J. 73, No. 1, 156-169 (2021) and Ukr. Mat. Zh. 73, No. 1, 138-148 (2021). MSC: 32W20 32J27 × Cite Format Result Cite Review PDF Full Text: DOI
Do, Hoang-Son; Le, Giang On the conditional plurisubharmonic envelopes of bounded functions. (English) Zbl 1480.32006 Int. J. Math. 32, No. 9, Article ID 2150060, 17 p. (2021). Reviewer: Marek Jarnicki (Kraków) MSC: 32U05 32W20 32T99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Jiaxiang; Wang, Xu-Jia; Zhou, Bin A priori estimate for the complex Monge-Ampère equation. (English) Zbl 1477.32062 Peking Math. J. 4, No. 1, 143-157 (2021). Reviewer: Rafał Czyż (Krakow) MSC: 32W20 35J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Benali, Amel; Zeriahi, Ahmed Erratum to: “The Hölder continuous subsolution theorem for complex Hessian equations”. (Erratum à : “Le théorème des sous-solutions Hölder continues pour les équations Hessiennes complexes”.) (English. French summary) Zbl 1539.31004 J. Éc. Polytech., Math. 8, 779-789 (2021). Reviewer: Martin Sera (Kyōto) MSC: 31C45 32U15 32U40 32W20 35J96 × Cite Format Result Cite Review PDF Full Text: DOI
Hai, Le Mau; Quan, Vu Van Hölder continuity for solutions of the complex Monge-Ampère type equation. (English) Zbl 1462.32042 J. Math. Anal. Appl. 494, No. 1, Article ID 124586, 14 p. (2021). Reviewer: Rafał Czyz (Krakow) MSC: 32U05 32W20 × Cite Format Result Cite Review PDF Full Text: DOI
Kołodziej, Sławomir; Nguyen, Ngoc Cuong An inequality between complex Hessian measures of Hölder continuous \(m\)-subharmonic functions and capacity. (English) Zbl 1452.32038 Chen, Jingyi (ed.) et al., Geometric analysis. In honor of Gang Tian’s 60th birthday. Cham: Birkhäuser. Prog. Math. 333, 157-166 (2020). Reviewer: Marek Jarnicki (Kraków) MSC: 32U05 × Cite Format Result Cite Review PDF Full Text: DOI
Benali, Amel; Zeriahi, Ahmed The Hölder continuous subsolution theorem for complex Hessian equations. (Le théorème des sous-solutions Hölder continues pour les équations Hessiennes complexes.) (English. French summary) Zbl 1528.31004 J. Éc. Polytech., Math. 7, 981-1007 (2020); erratum ibid. 8, 779-789 (2021). Reviewer: Martin Sera (Kyōto) MSC: 31C45 32U15 32U40 32W20 35J96 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kołodziej, Sławomir; Sroka, Marcin Regularity of solutions to the quaternionic Monge-Ampère equation. (English) Zbl 1446.32023 J. Geom. Anal. 30, No. 3, 2852-2864 (2020). Reviewer: Marek Jarnicki (Kraków) MSC: 32U05 35D30 × Cite Format Result Cite Review PDF Full Text: DOI
Kołodziej, Sławomir; Nguyen, Ngoc Cuong A remark on the continuous subsolution problem for the complex Monge-Ampère equation. (English) Zbl 1436.32119 Acta Math. Vietnam. 45, No. 1, 83-91 (2020). MSC: 32W20 32U40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Ngoc Cuong On the Hölder continuous subsolution problem for the complex Monge-Ampère equation. II. (English) Zbl 1442.32045 Anal. PDE 13, No. 2, 435-453 (2020). Reviewer: Eleonora Di Nezza (Bures-sur-Yvette) MSC: 32W20 32U05 32T15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Do, Hoang-Son; Le, Giang; Tô, Tat Dat Viscosity solutions to parabolic complex Monge-Ampère equations. (English) Zbl 1436.32106 Calc. Var. Partial Differ. Equ. 59, No. 2, Paper No. 45, 35 p. (2020). MSC: 32U15 32U05 32T15 32W20 35K96 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bouhssina, Manar On the regularity of complex Hessian equation on \(m\)-hyperconvex domain. (English) Zbl 1421.32044 Complex Var. Elliptic Equ. 64, No. 10, 1739-1755 (2019). MSC: 32W20 32U05 × Cite Format Result Cite Review PDF Full Text: DOI
Boukhari, Fadoua Hölder continuous solutions to quaternionic Monge-Ampère equations. (English) Zbl 1421.30062 J. Math. Anal. Appl. 477, No. 1, 747-768 (2019). MSC: 30G35 35J96 32T15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kołodziej, Sławomir; Nguyen, Ngoc Cuong Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds. (Solutions continues Höldériennes de l’équation de Monge-Ampère sur les variétés hermitiennes compactes.) (English. French summary) Zbl 1419.53070 Ann. Inst. Fourier 68, No. 7, 2951-2964 (2018). MSC: 53C55 35J96 32U40 × Cite Format Result Cite Review PDF Full Text: arXiv
Nguyen Xuan Hong; Tran Van Thuy Hölder continuous solutions to the complex Monge-Ampère equations in non-smooth pseudoconvex domains. (English) Zbl 1402.32041 Anal. Math. Phys. 8, No. 3, 465-484 (2018). MSC: 32W20 32U05 32T99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Ngoc Cuong On the Hölder continuous subsolution problem for the complex Monge-Ampère equation. (English) Zbl 1388.32029 Calc. Var. Partial Differ. Equ. 57, No. 1, Paper No. 8, 15 p. (2018). Reviewer: Gabor Etesi (Budapest) MSC: 32W20 32U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Feng, Ke; Shi, Ya Long; Xu, Yi Yan On the Dirichlet problem for a class of singular complex Monge-Ampère equations. (English) Zbl 1396.32020 Acta Math. Sin., Engl. Ser. 34, No. 2, 209-220 (2018). Reviewer: Slawomir Kołodziej (Kraków) MSC: 32W20 35J75 53C55 × Cite Format Result Cite Review PDF Full Text: DOI
Baracco, Luca; Khanh, Tran Vu; Pinton, Stefano The complex Monge-Ampère equation on weakly pseudoconvex domains. (L’équation de Monge-Ampère complexe sur les domaines faiblement pseudo-convexes.) (English. French summary) Zbl 1373.32030 C. R., Math., Acad. Sci. Paris 355, No. 4, 411-414 (2017). Reviewer: Slawomir Kołodziej (Kraków) MSC: 32W20 32U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Baracco, Luca; Khanh, Tran Vu; Pinton, Stefano; Zampieri, Giuseppe Hölder regularity of the solution to the complex Monge-Ampère equation with \(L^p\) density. (English) Zbl 1361.32045 Calc. Var. Partial Differ. Equ. 55, No. 4, Paper No. 74, 8 p. (2016). Reviewer: Rafał Czyz (Krakow) MSC: 32W20 32U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Eyssidieux, Philippe; Guedj, Vincent; Zeriahi, Ahmed Weak solutions to degenerate complex Monge-Ampère flows. I. (English) Zbl 1322.35094 Math. Ann. 362, No. 3-4, 931-963 (2015). Reviewer: Slawomir Kołodziej (Kraków) MSC: 35K96 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Charabati, Mohamad Hölder regularity for solutions to complex Monge-Ampère equations. (English) Zbl 1330.32012 Ann. Pol. Math. 113, No. 2, 109-127 (2015). Reviewer: Slawomir Kołodziej (Kraków) MSC: 32W20 32T99 32U15 35J96 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinh, Tien-Cuong; Nguyên, Viêt-Anh Characterization of Monge-Ampère measures with Hölder continuous potentials. (English) Zbl 1305.32018 J. Funct. Anal. 266, No. 1, 67-84 (2014). Reviewer: Slawomir Kołodziej (Kraków) MSC: 32U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Ngoc Cuong Hölder continuous solutions to complex Hessian equations. (English) Zbl 1302.32034 Potential Anal. 41, No. 3, 887-902 (2014). Reviewer: Slawomir Kołodziej (Kraków) MSC: 32U05 32U40 35J99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zeriahi, Ahmed A viscosity approach to degenerate complex Monge-Ampère equations. (English. French summary) Zbl 1334.32016 Ann. Fac. Sci. Toulouse, Math. (6) 22, No. 4, Spec. Issue, 843-913 (2013). MSC: 32W20 32J27 32Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berman, Robert J.; Berndtsson, Bo Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties. (English. French summary) Zbl 1283.58013 Ann. Fac. Sci. Toulouse, Math. (6) 22, No. 4, Spec. Issue, 649-711 (2013). MSC: 58J05 53C44 35J96 14M25 58J32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lu, Hoang Chinh Solutions to degenerate complex Hessian equations. (English) Zbl 1288.53072 J. Math. Pures Appl. (9) 100, No. 6, 785-805 (2013). Reviewer: Maria Falcitelli (Bari) MSC: 53C55 32Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinew, Sławomir Hölder continuous potentials on manifolds with partially positive curvature. (English) Zbl 1207.32034 J. Inst. Math. Jussieu 9, No. 4, 705-718 (2010). Reviewer: Alexandr Yu. Rashkovsky (Stavanger) MSC: 32W20 32U15 53C55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinew, Sławomir; Zhang, Zhou On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds. (English) Zbl 1210.32020 Adv. Math. 225, No. 1, 367-388 (2010). Reviewer: Alexandr Yu. Rashkovsky (Stavanger) MSC: 32W20 32U05 32U40 53C55 × Cite Format Result Cite Review PDF Full Text: DOI
Guedj, Vincent; Zeriahi, Ahmed The weighted Monge-Ampère energy of quasiplurisubharmonic functions. (English) Zbl 1143.32022 J. Funct. Anal. 250, No. 2, 442-482 (2007). Reviewer: Paolo Cascini (Santa Barbara) MSC: 32W20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv