Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

By Filippo Bracci, Manuel D. Contreras, S. Díaz-Madrigal. 2006

48 citations recorded by the source corpus.

We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of semigroups. Among other things, we characterize boundary regular fixed points both in terms of the boundary behavior of infinitesimal generators and in terms of pluripotential theory.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/bd16255e23cb17f16ab885f18d4024346c15071c

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In Applied Mathematics

1. Filippo Bracci
2. Manuel D. Contreras
3. S. Díaz-Madrigal
4. B. Filippo
5. Leandro Arosio
6. H. Hamada
7. G. Kohr

Citations in the corpus

• Evolution families and the Loewner equation I: the unit disc (2008, methodology): “Therefore ðdrDÞðfs; zðtÞ;fs;wðtÞÞ G fs; zðtÞ; t ;G fs;wðtÞ; t e 0 for almost every t A 1⁄20;þyÞ by [6], Theorem 0.”
• Evolution families and the Loewner equation II: complex hyperbolic manifolds (2008, background): “Remark 3 According to [3] if M = D is a strongly convex domain inCn with smooth boundary then G is a Herglotz vector field if and only if it is a weak holomorphic vector field such that for almost every t ∈ [0,+∞) the function D z → G(z, t) is an infinitesimal generator of a semigroup of holomorphic”