Recent progress on geometric analysis and Riemannian geometry: The geometry of pp-waves
Presenter
October 21, 2024
Keywords:
- mean curvature flow
- Ricci flow
- fully nonlinear flows
- general relativity
- mass
- Ricci curvature
- scalar curvature
- sectional curvature
- symmetry
- Riemannian geometry
- groups actions
- minimal surfaces
- stability
MSC:
- 35-XX - Partial differential equations
- 49-XX - Calculus of variations and optimal control
- optimization
- 53-XX - Differential geometry
- 58-XX - Global analysis
- analysis on manifolds
- 83-XX - Relativity and gravitational theory
Abstract
In Special Relativity, the vanishing of mass occurs exclusively in the cases of vacuum and radiation. In this talk, we demonstrate that an analogous result holds within the framework of General Relativity. The proof combines ideas from spin geometry and spacetime harmonic functions. This is based upon joint work with Yiyue Zhang.