The research of Alessandro Carlotto lies at the interface of Differential Geometry, Nonlinear Analysis and Mathematical Physics, with special focus on geometric variational problems arising in contexts ranging from general relativity to conformal geometry.
Some specific topics include:
Positive scalar curvature (moduli spaces of metrics, rigidity phenomena, extensions and fill-ins, weak notions)
Einstein constraint equations (solvability via gluing methods, localization of initial data sets, construction of exotic N-body solutions)
Geometry of asymptotically flat spaces (effective versions of the positive mass theorem, isoperimetric notions of mass, minimal planes)
Minimal surfaces (sharp compactness criteria, generic finiteness, gap results, Morse index estimates involving topological invariants)
Liouville equations (Morse-theoretic analysis, curvature prescription in presence of conical singularities, asymptotic non-existence results)
- Yamabe flows (rate of convergence vs. Morse type of Yamabe-critical points, slowly converging flows, peculiar geometric applications)
A list of scientific publications is provided via this link.