Research

My research lies at the intersection of partial differential equations and differential geometry, with a particular focus on geometric analysis and conformal geometry. I am interested in elliptic and degenerate elliptic equations, calculus of variations, critical Sobolev inequalities, compactness phenomena, and the regularity of solutions.

My work focuses on the Yamabe problem, and its variants. In particular, I study qualitative properties of minimizers and solution sets, such as stability and compactness, as well as related questions involving conformally covariant operators and geometric variational problems.