arXiv research

The paper establishes a majorization result for symmetric matrices.

Formula establishes determinant majorization for symmetric matrices.

Study estimates eigenvalues for concave Hessian operators on convex domains.

Solves curvature problems on manifolds with negative curvature.

Estimates for polynomial operators using determinant majorization and subharmonics.

The Special Lagrangian Potential Equation for a function $u$ on a domain $Ω\subset {\bf R}^n$ is given by ${\rm tr}\{\arctan(D^2 \,u) \} = θ$ for a contant $θ\in (-n {π\over 2}, n {π\over 2})$. For $C^2$ solutions the graph of $Du$ in $Ω\times {\bf R}^n$ is a special Lagrangian submanfold. Much has been understood abou…