The Pansu conjecture asserts that the Pansu balls minimize horizontal perimeter among measurable sets of fixed volume in the first Heisenberg group.
Chen et al. (2026) reported the unrestricted sharp isoperimetric inequality
 |
for 
and finite horizontal perimeter 
, with equality iff 
agrees with a Pansu ball except
on a set of measure zero. Here 
is Lebesgue measure in
the coordinates and normalization used in the definition
of a Pansu ball.
Chen et al. (2026) state that ChatGPT 6.0 Astra assisted in refining their earlier proof strategy and performing calculations, all of which they independently reviewed and verified.
