Monotonicity conjecture for the turning angle of positive--parameter self-shrinkers

Let

$$be a positive parameter, let$$

denote the energy, and let

$$be the turning-angle function associated with the corresponding one-dimensional$$

-self-shrinker solution. Monotonicity conjecture. When $>0$,

$$is monotonically decreasing with respect to$$

.

This extends the monotonicity known for the self-shrinker case $=0$, attributed here to Abresch and Langer. The claim is presented as a conjecture based on numerical simulations; no proof or resolution is supplied in the source.