Controlled Loewner-Kufarev equation embedded into the universal Grassmannian. (English) Zbl 1459.35363
The authors introduce and study a class of controlled Loewner-Kufarev equations. The main result of the paper is the explicit formula of the solution in terms of the signature of the driving function through the action of words in generators of the Witt algebra.
Reviewer: Mohamed Majdoub (Dammam)
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 30F10 | Compact Riemann surfaces and uniformization |
| 35C10 | Series solutions to PDEs |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
| 93C20 | Control/observation systems governed by partial differential equations |
| 30C25 | Covering theorems in conformal mapping theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
Keywords:
Loewner-Kufarev equation; Grassmannian; conformal field theory; Witt algebra; free probability theory; Faber polynomial; Grunsky coefficient; signatureReferences:
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