Nonlinear Resolvents and Decreasing Loewner Chains

In this article,we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of C n are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on unbounded convex domains in C . In the case of the upper half-plane,...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-04, Vol.34 (4), Article 99
Main Authors: Hotta, Ikkei, Schleißinger, Sebastian, Sugawa, Toshiyuki
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Half planes
Mathematics
Mathematics and Statistics
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Summary:In this article,we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of C n are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on unbounded convex domains in C . In the case of the upper half-plane, we obtain a complete solution by using that nonlinear resolvents of certain generators correspond to semigroups of probability measures with respect to free convolution.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01544-y