Problems to reduce from to prove an $\Omega(n\log n)$ lower bound
Ben-Or directly proved  $\Omega(n\log n)$ lower bounds for several fundamental problems in the algebraic computation tree model:


Element distinctness: Given an array of $n$ real numbers, are its elements distinct?
Set disjointness: Given two sets of $n$ real numbers, do they have an element in common?
Set equality: Given two sets of $n$ real numbers, is one array a permutation of the other?
Measure problem: Given $n$ real intervals, what is the total length of their union?
Set inclusion: Given two sets of real numbers, is one a subset of the other?
Permutation Parity: Given an permutation of the set $[n]$, is the permutation even or odd?


The first three are the ones most often used in computational geometry.