Karim RAKHIMOV

Research

Publications

 With F. Bianchi, T.-C. Dinh,   Hölder continuity and laminarity of the Green currents for Hénon-like maps , Journal of the Institute of Mathematics of Jussieu (accepted) (2026),  arXiv 

Flat structure of meromorphic connections on Riemann surfaces, Journal of Geometric Analysis , (2025)  arXiv  

With S. Bazarbaev, F. Bianchi,   On the support of measures of large entropy for polynomial-like maps. Anal.Math.Phys. 15, 69 (2025)

With M. Abate,  Dynamics of Fuchsian meromorphic connections with real periods  arXiv (2024)

With M. Brevard,  Propagation of equilibrium states for stable holomorphic families of endomorphisms of Pk  arXiv (2024)

 With F. Bianchi, T.-C. Dinh, Monotonicity of dynamical degrees for Hénon-like and polynomial-like maps, Transactions of the American Mathematical Society 377 (09), 6595-6618,  arXiv (2024)

With F. Bianchi, Strong probabilistic stability in holomorphic families of endomorphisms of Pk and polynomial-like maps,  International Mathematics Research Notices, Volume 2024, Issue 12, June 2024, Pages 9875–9892, 

With Sh. Shopulatov,  A mean value criterion for plurisubharmonic functions, Complex Variables and Elliptic Equations, 67(12), 2866–2877, arXiv (2021)

 With A. Sadullaev, S. Imamkulov,  Bounded subharmonic function posses the Lebesque property in each point. Math. Notes. (Russia), Vol.96, No.6 (2014), 

 With A. Sadullaev, Capacity dimension of Brjuno set.  Indiana University Mathematics journal, volume 64, number 6 (2015), 

 Capacity dimension of Perez-Marco set. Contemporary Mathematics, Volume 662 (2016), 

 Cn-capacity defined with Laplacian (in Russian), Uzbek mathematical journal. 2012. No.2. 

 Cn-capacity,  based on plurisubharmonic functions (in Russian), Reports of the academy of sciences. 2012. 

Books

With A. Pirnapasov, Kh. Egamberganov, UZSML & Nabla Olimpiadalari, KAX series, 2020 (in Uzbek)

With A. Azizov, Analizning nostandart masalalari, KAX series, 2021 (in Uzbek) preprint