Dinh, Tien-Cuong; Sibony, Nessim Regularization of currents and entropy. (English) Zbl 1074.53058 Ann. Sci. Éc. Norm. Supér. (4) 37, No. 6, 959-971 (2004). Authors’ summary: Let \(T\) be a positive closed \((p,p)\)-current on a compact Kähler manifold \(X\). We prove the existence of smooth positive closed \((p,p)\)-forms \(T_ n^ +\) and \(T_ n^ -\) such that \(T_ n^ + - T_ n^ -\to T\) weakly. Moreover, \(\| T_ n^ \pm\| \leq c_ X\| T\| \) where \(c_ X >0\) is a constant independent of \(T\). We also extend this result to positive pluriharmonic currents. Then we study the wedge product of positive closed \((1,1)\)-currents having continuous potential with positive pluriharmonic currents. As an application, we give an estimate for the topological entropy of meromorphic maps on compact Kähler manifolds. Reviewer: Witold Mozgawa (Lublin) Cited in 3 ReviewsCited in 40 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32U40 Currents 32C30 Integration on analytic sets and spaces, currents 37B40 Topological entropy 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 32H04 Meromorphic mappings in several complex variables 32Q15 Kähler manifolds Keywords:\((p,p)\)-current; Kähler manifold; weak convergence; pluriharmanic current; bounded potential PDF BibTeX XML Cite \textit{T.-C. Dinh} and \textit{N. Sibony}, Ann. Sci. Éc. Norm. Supér. (4) 37, No. 6, 959--971 (2004; Zbl 1074.53058) Full Text: DOI arXiv Numdam Numdam EuDML OpenURL References: [1] Alessandrini L. , Bassanelli G. , Plurisubharmonic currents and their extension across analytic subsets , Forum Math. 5 ( 6 ) ( 1993 ) 577 - 602 . 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