Research  interests

A central question in geometric analysis is the search for distinguished or “optimal” metrics on a given Riemannian manifold. This problem lies at the intersection of differential geometry, partial differential equations, and mathematical physics, and provides the unifying framework of my research.

A paradigmatic example is the Yamabe problem, which asks for the existence of constant scalar curvature metrics within a given conformal class and leads to a nonlinear elliptic equation with critical Sobolev growth. Motivated by this and related questions in conformal geometry, my research focuses on nonlinear elliptic and geometric PDEs on Riemannian manifolds involving critical and supercritical nonlinearities.

More recently, my work has expanded to include higher-order conformally invariant operators, such as the Paneitz–Branson operator and equations involving Q-curvature, as well as the study of Einstein metrics on warped and multiply warped product manifolds. I am particularly interested in variational methods, obstruction results, and rigidity phenomena, and in understanding how geometric and topological constraints influence the existence and qualitative behavior of solutions.