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In this article we prove that nonlinear resolvents of infinitesimalgenerators on bounded and convex subdomains of $\C^n$ are decreasing Loewnerchains. Furthermore, we consider the problem of the existence of nonlinearresolvents on unbounded convex domains in $\C$. In the case of the upperhalf-plane, we obtain a complete solution by using that nonlinear resolvents ofcertain generators correspond to semigroups of probability measures withrespect to free convolution.

Nonlinear resolvents and decreasing Loewner chains