The boundary of the Mandelbrot set has Hausdorff dimension two
Complex analytic methods in dynamical systems - IMPA, January 1992, Astérisque, no. 222 (1994), pp. 389-405 
@incollection{AST_1994__222__389_0,
     author = {Shishikura, Mitsuhiro},
     title = {The boundary of the {Mandelbrot} set has {Hausdorff} dimension two},
     booktitle = {Complex analytic methods in dynamical systems - IMPA, January 1992},
     editor = {Camacho C. and Lins Neto A. and Moussu R. and Sad P.},
     series = {Ast\'erisque},
     pages = {389--405},
     year = {1994},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {222},
     mrnumber = {1285397},
     zbl = {0813.58047},
     language = {en},
     url = {https://www.numdam.org/item/AST_1994__222__389_0/}
}
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Shishikura, Mitsuhiro. The boundary of the Mandelbrot set has Hausdorff dimension two, dans Complex analytic methods in dynamical systems - IMPA, January 1992, Astérisque, no. 222 (1994), pp. 389-405. https://www.numdam.org/item/AST_1994__222__389_0/

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