3 papers
math.AP2026
Quasiconvexity of the Burkholder function on symmetric matrices
André Guerra
We use Morse Theory to prove that the Burkholder function is quasiconvex on symmetric matrices, which implies several sharp inequalities for the Beurling--Ahlfors transform when ac…
math.AP2024
Lower semicontinuity, Stoilow factorization and principal maps
Kari Astala, Daniel Faraco, André Guerra +2
We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as…
math.AP2023
The local Burkholder functional, quasiconvexity and Geometric Function Theory
Kari Astala, Daniel Faraco, André Guerra +2
We show that the local Burkholder functional is quasiconvex. In the limit of going to 2 we find a class of non-polyconvex functionals which are quasiconvex on th…