A rank-one convex function is a real-valued function 
on the space of 
real matrices whose restriction to every line with a
direction of matrix rank one is a convex
function. Equivalently, 
is a convex
function for every matrix 
and all vectors 
,
.
Here 
denotes the transpose (Morrey 1952). Quasiconvexity
implies rank-one convexity for continuous functions.
Conti et al. (2026) constructed a smooth function 
that is rank-one convex but not quasiconvex, even
though 
for every 
and 
.
The special orthogonal group 
acts here by left multiplication. This invariance is called
frame indifference. The example does not have invariance under right multiplication
by rotations.
Conti et al. (2026) report mathematical assistance from Claude Opus 5.5 and a Lean 4 formalization of their main results written by that model under their guidance.
