Abstract:
We prove some generalizations and analogs of the Harnack inequalities for pluriharmonic, holomorphic and “almost holomorphic” functions. The results are applied to proving smoothness properties of holomorphic motions over almost complex manifolds.
This publication is cited in the following 8 articles:
B. N. Khabibullin, E. U. Taipova, “Lower Estimates for Subhramonic Functions and the Harnack Distance”, J Math Sci, 260:6 (2022), 833
E. M. Chirka, “Capacities on a Compact Riemann Surface”, Proc. Steklov Inst. Math., 311 (2020), 36–77
E. M. Chirka, “Equilibrium Measures on a Compact Riemann Surface”, Proc. Steklov Inst. Math., 306 (2019), 296–334
E. M. Chirka, “Potentials on a compact Riemann surface”, Proc. Steklov Inst. Math., 301 (2018), 272–303
A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1137–1144
Adel Khalfallah, “Old and New Invariant Pseudo-Distances Defined by Pluriharmonic Functions”, Complex Anal. Oper. Theory, 9:1 (2015), 113
P. V. Dovbush, “Estimates for Holomorphic Functions with Values in C\{0,1}”, APM, 03:06 (2013), 586
E. M. Chirka, “Holomorphic motions and uniformization of holomorphic families of Riemann surfaces”, Russian Math. Surveys, 67:6 (2012), 1091–1165
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