Titlebook: Analytic Continuation and q-Convexity; Takeo Ohsawa,Thomas Pawlaschyk Book 2022 The Author(s), under exclusive license to Springer Nature

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Postdisciplinary Studies in Discourseies. Based on this, Grauert was interested in cohomology of complex spaces and used the .-convexity as a boundary condition in the spirit of Levi and in terms of exhaustion functions. Meanwhile, Fujita investigated the continuity principle on . or . . − .. Tadokoro pointed out that these notions are indeed equivalent.

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Postdisciplinary Studies in Discourseis reason, it contains both classical and the author’s recent results on the topic of .-plurisubharmonic functions. It serves as a preparation for Chap. . in which we study domains created by . functions. These were introduced by Hunt and Murray in 1978 who defined them in terms of a local maximum p

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Juliet Langman,Holly Hansen-Thomasti and Grauert (1962). Andreotti–Grauert’s finiteness theorem was applied by Andreotti and Norguet (1966–1971) to extend Grauert’s solution of the Levi problem to .-convex spaces. A consequence is that the sets of (. − 1)-cycles of .-convex domains with smooth boundary in projective algebraic manifo

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Analytic Continuation and Classical Pseudoconvexity,vex domains, the latter defined by plurisubharmonic functions. In the first half of the twentieth century, intense research on these objects accumulated in the groundbreaking proof of Levi’s conjecture by Oka in 1942 on the equivalence of these two types of domains.