AI 中文总结
该研究运用Morse理论证明Burkholder函数及Székelyhidi引入的分离函数在对称矩阵上具有拟凸性，由此得到Beurling–Ahlfors变换作用于实值函数的若干尖锐不等式。
AI 中文摘要
我们运用Morse理论证明Burkholder函数在对称矩阵上是拟凸的，这意味着Beurling–Ahlfors变换作用于实值函数时存在若干尖锐不等式；更一般地，我们证明Székelyhidi引入的分离函数在对称矩阵上是拟凸的。
英文摘要
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 acting on real-valued functions. More generally, we prove that the separating functions introduced by Székelyhidi are quasiconvex on symmetric matrices.
Comments16 pages, comments welcome!
