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We construct an analogue of W. Thurston's "Master teapot" for each principalvein in the Mandelbrot set, and generalize geometric properties known for thecorresponding object for real maps. In particular, we show that eigenvaluesoutside the unit circle move continuously, while we show "persistence" forroots inside the unit circle. As an application, this shows that the outsidepart of the corresponding "Thurston set" is path connected. In order to dothis, we define a version of kneading theory for principal veins, and we provethe equivalence of several algorithms that compute the core entropy.

Master Teapots and Entropy Algorithms for the Mandelbrot Set