Evolution families and the Loewner equation II: complex hyperbolic manifolds
By Filippo Bracci, Manuel D. Contreras, S. Díaz-Madrigal. 2008
99 citations recorded by the source corpus.
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type differential equation on manifolds.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7c3dc2330402f1a4b6053ffdaa0b610d5a1944d8
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In Applied Mathematics
- Filippo Bracci
- H. Hamada
- G. Kohr
- Manuel D. Contreras
- S. Díaz-Madrigal
- Leandro Arosio
- B. Filippo
- Marco Abate
In Mathematical Physics
- Filippo Bracci
- Manuel D. Contreras
- S. Díaz-Madrigal
- Leandro Arosio
- Marco Abate
- H. Hamada
- G. Kohr
- B. Filippo
Citations in the corpus
- An abstract approach to Loewner chains (2010, methodology): “ almost every t ≥ 0 the holomorphic vector field z → G(z,t) is semicomplete (this is proved in [5] for strongly convex domains, but the same proof works in the complete hyperbolic case). The result in [4] which we will use in the sequel is the following: Theorem 2.6. Let Mbe a complete hyperbolic com”
- Evolution families and the Loewner equation I: the unit disc (2008, methodology): “1 holds more generally on complex complete hyperbolic manifolds (see [5]).”
- The evolution of Loewner's differential equations (2010, methodology): “Hamada and others [25], [24], [17], [12].”