Questions, not proof records
Each statement record keeps the mathematical question, a dated status source, accessible references, and any pinned Lean formulation separate from proof verification.
sorry marks an admitted statement, not a proof. Source indexing does not mean the formulation has been independently built or certified by Therefore.Conjecture 1.3* (the conjecture): the only atomless Borel probability measure on which is both - and -invariant is the Lebesgue measure.
The MLC conjecture, stating that the mandelbrot set is locally connected.
A stronger version of the MLC conjecture, stating that all multibrots are locally connected.
Note that we don't need to require 2 ≤ n because the conjecture holds in the trivial cases n = 0
and n = 1 too.
The density of hyperbolicity conjecture, stating that the set of all parameters c for which
fun z ↦ z ^ 2 + c has an attracting cycle is dense in the Mandelbrot set.
The density of hyperbolicity conjecture for Multibrot sets, stating that the set of all
parameters c for which fun z ↦ z ^ n + c has an attracting cycle is dense in multibrotSet n.
Note that we need to require 2 ≤ n because the conjecture is trivially false for n = 1.
The boundary of the Mandelbrot set is conjectured to have zero area.
The boundary of any Multibrot set is conjectured to have zero area.
Note that we don't need to exclude the trivial cases n = 0 and n = 1 because the conjecture
holds for them.