Research

My main research areas are partial differential equations and geometric analysis, with a particular focus on conformal geometry. Within these areas, I am interested in elliptic PDEs and variational methods, along with sharp Sobolev inequalities, compactness phenomena, and regularity theory.

My work so far has been related to the Yamabe problem and its variants, particularly the boundary and fractional Yamabe problems. In this setting, I have studied the stability of minimizers, while my broader interests include compactness and other qualitative properties of minimizers and solution sets, as well as related questions involving conformally covariant operators and geometric variational problems.