I am Rodrigo Avalos, a mathematician working in differential geometry, geometric analysis, partial differential equations, and mathematical general relativity. I am currently a permanent member of the academic staff (unbefristeter wissenschaftlicher Mitarbeiter) at the Institut für Mathematik, University of Rostock.
My research focuses on geometric partial differential equations arising in conformal geometry and general relativity. I am particularly interested in the Yamabe problem and related conformal equations, regularity questions for geometric structures of low regularity, asymptotically Euclidean manifolds, the Einstein constraint equations, and geometric invariants associated with isolated gravitational systems.
Before joining the University of Rostock, I was a postdoctoral researcher at the University of Tübingen and an Alexander von Humboldt Postdoctoral Fellow at the Universities of Tübingen and Potsdam.
Research Interests
- Geometric Analysis and Elliptic PDEs
- Conformal Geometry and the Yamabe Problem
- Mathematical General Relativity
- Asymptotically Euclidean Manifolds
- Einstein Constraint Equations
- Scalar and Q-Curvature Deformations
- Positive Mass and Positive Energy Theorems
- Asymptotic Invariants of Isolated Gravitational Systems