G-BSDEs with mean constraints in time-dependent intervals

In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by G-Brownian motions (G-BSDEs), where G-expectations are constrained in some time-dependent intervals. To establish well-posedness results, we firstly construct a backward Skorokhod problem with sublinear expectation, and then apply that in the study of doubly mean-reflected G-BSDEs involving Lipschitz and quadratic generators under bounded and unbounded terminal conditions. Also we utilize fixed-point argumentations and -methods while solving these equations. Finally, we extend the results to multi-dimensional doubly mean-reflected G-BSDEs with diagonal generators.