Self-improvement phenomena

Self-improvement phenomena are important both for theoretical and practical reasons. In analysis of metric spaces, Keith and Zhong on the one hand and Lewis on the other proved foundational self-improvement results. Their results are hard, and the realization of this project has been that all of these self-improvement results can be cast in the same framework as a task of constructing a “sufficiently good curve”, which is obtained via an iteration based on filling and choosing an appropriate level. The new insights gained allow for a new weighted result with Vähäkangas and Lehrbäck, which was not known before. It further gives a way of fairly directly obtaining the full strength of Keith and Zhong as well as Lewis, with essentially sharp bounds on the self-improvement.


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