The pluricomplex Poisson kernel for strongly pseudoconvex domains

Rooftop envelopes and residual plurisubharmonic functions

“…Furthermore, it was shown in [10], [26], [11] In the cases presented in Example 3.2, we have g ϕ = g o ϕ and g b ϕ = 0, while the latter property is far from being true when L(ϕ) is not compactly supported inside the domain.…”

Dr. Strangelove or: how I learned to stop worrying and love the citations

“…Obviously, the most citations of your works, no matter if already published, if pre-print [31,32,33,42] or future [4,7,8,10,11,20,35,43], you get to put in the bibliography, the better it is. And remember that also citations to pre-prints or future papers will work: you just have to remember to show the citation to Scopus or Web Of Science.…”

Parameter dependence of complex geodesics and its applications

“…Next, we turn to some consequences of the preceding results, especially an application to the higher regularity of solutions to the complex Monge-Ampère equation considered in [BP05,BPT09,BST21,HW20]. To this end, we first need to recall the so-called boundary spherical representation for Ω constructed by Huang and the author in [HW20].…”

“…The higher regularity of solutions to the complex Monge-Ampère equation considered in the paper will be obtained, as Lempert [Lem81,Lem83,Lem86] did, by studying the associated complex foliation, whose leaves are precisely complex geodesic discs initiated from a fixed boundary point. Our method is also inspired by the work of Huang [Hua94b] and Bracci and his collaborators [BP05,BPT09,BST21].…”

“…which has been extensively studied in the literature (see, e.g., [Zah84, Kli85, Dem87, BD88, Gua98, Her00, B lo00, B lo05] among others) after the seminal work of Lempert [Lem81]; whose solution is easily proved to be unique, now known as the pluricomplex Green function, sharing many properties with the classical Green function and having profound applications, notably when it appears as the weight function in the Hörmander's L 2 theory of the ∂-operator (see [DO95, Che99, Her99, BP00, CZ02, B lo05, CF11, B lo13, Che14, Che17], etc). The study of equation (1.5) was initiated in [BP05,BPT09] and continued very recently in [HW20,BST21]. It turns out that the function P Ω ( • , p) constructed as above shares many properties with the classical Poisson kernel (see [BP05,BPT09]) and has already found applications to the theory of holomorphic semigroups (see [BCD10] and also the survey [Bra10]) and others.…”