Vitushkin's quasiadditivity conjecture for continuous analytic capacity

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Let K1K_1 and K2K_2 be compact subsets of the plane, and let α\alpha denote continuous analytic capacity. Vitushkin's quasiadditivity conjecture. There exists a constant CC such that

α(K1∪K2)≤C(α(K1)+α(K2)),\alpha(K_1\cup K_2) \le C\left(\alpha(K_1)+\alpha(K_2)\right),

for all compact sets K1K_1 and K2K_2. This conjecture arises from Vitushkin's localization method for rational approximation and would give a quasiadditivity principle for continuous analytic capacity. The supplied text does not indicate whether it has been resolved.

References

Primary source

Joan Verdera, “Birth and life of the L^2 boundedness of the Cauchy Integral on Lipschitz graphs”, arXiv:2109.06690 (2021).

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